As the other poster suggested, perhaps it is a hot-air craft ??
For reasons I hope others have explained clearly enough by now, that would be dumb.
Hot air could in theory be heated up well enough to compete with helium. The necessary temperature, at sea level, would be--well, how high do we want to go?
With helium, the maximum altitude you want to reach without having to vent gas is your
pressure height. As you rise, the gas expands; at pressure height your helium fills the available volume completely. Therefore that is the most helium you can load aboard down at sea level; any more and you will lose the excess if you ascend to pressure height. (Or, your pressure height with the extra gas is lower).
Blimps typically are filled 3/4 full at sea level, for a pressure height of 10,000 feet/3 kilometers. That is the altitude above which the FAA requires that passengers either be given oxygen masks or the cabin be pressurized.
The big US rigids operated by the Navy typically were filled for lower altitudes, giving them more lift but limiting their vertical range.
So let's say you want to compete with helium using hot air, and want as much lift as a 3/4 full at sea level helium ship can achieve. Well, 1 cubic meter of absolutely pure helium lifts a bit over 1 kilogram at sea level; allow for some helium impurity to make it exactly 1.
Air at sea level, in the "standard atmosphere," masses 1.224 kg/cubic meter. (Thus that, by the way, is the absolute upper limit of static lift available at sea level, even if you use a magic volume that is completely weightless and infinitely strong). To get .75 kg of lift by heating air, the air must mass 0.474, so you need to raise its temperature to 2.58 times the ambient; in the standard atmosphere this is assumed to be 285 degrees Kelvin. It comes to 734 Kelvin, which is 462 Celsius or 865 Fahrenheit.
That doesn't sound so bad, considering that it is after all air--it might not be inconceivable to make some kind of light structure that can stand that kind of heat and slow down heat losses enough that a good heat source can compensate, but we aren't done yet. The helium ship has the same lift all the way from the surface to pressure height; we need to match that. At 3 kilometers up, the temperature has fallen 19.5 degrees (Celsius or Kelvin) due to the adiabatic lapse rate--this will help. But density has fallen to 3/4--that will not! Now the density is 0.918; the hot air must be heated to lower its density to 0.168. So we have 255.5 degrees K * 5.46 = 1396 K, which is 1123 C or 2054 K.
That, I think you will agree, is darn hot.
(And by the way, to match the lift of helium with a very low pressure height helium cell--ie, one almost full at sea level--one needs to raise the temperature at least that much at sea level).
Trying to estimate just how what heat loss rate these temperatures imply is pretty far beyond me. Aside from the question of whether sufficiently lightweight materials can even hold air this hot without melting, burning, or failing for some other chemical reason, the fact is some heat will leak out, even if our structure includes a fair amount of insulation, and to keep it warm that heat needs to be constantly replaced. At what rate--depends on the inside temperature, outside temperature, surface area, and--here is the imponderable--the dynamic response of heated air to the heat itself. Wind conditions will presumably matter but it is hard to estimate just how.
It could well be that a hot air lift bag is still superior in power terms to using the same power you convert to heat to instead power some kind of dynamic thruster.
Going the other way--trying to get better lift than helium, even at sea level, is a mug's game. If you doubled the already-very-high temperature needed at sea level, you'd match the lift of hydrogen at 3/4 the volume sea level (that is, full at a pressure height of 3 kilometers). Which as pointed out is just an 8 percent improvement over helium.
You could moderate the temperatures by settling for a lesser lift. But that raises the necessary volume for a given payload, meaning more structural area to lose heat through and more structural mass too. It also raises drag if you propose to propel the thing.
Anyway, there is yet another lift gas available--steam. Water weighs 18 atomic mass units to the atmospheric gases (mainly nitrogen and oxygen) 29-30; also it must be hot to be a vapor, so there is an additional thermal reduction in density as well. The upshot is, at sea level saturated steam has 60 percent of the lift of helium. Also, you could carry some extra water to boil to get more lift if you need it, and allow it to condense to lower the lift. Actually, it will always be condensing anyway (but at a surprisingly low rate!) so to maintain lift, you would need to reboil it. Or enclose your steam cell in air heated above boiling temperature, but that heat will still leak away--however if you are propelling the airship the engines will put out waste heat anyway, so that heat might not cost anything extra. Meanwhile, if you do allow condensation, you not only remove the lift of the steam, you get back the weight of the water--so actually allowing 1 cubic meter of steam to condense is a net weight increase (loss of lift plus weight of water) of 1.225 kilograms.
The possible utility of hot air in a practical sense would be to get some variable lift; using steam for that purpose instead strikes me as more advantageous. There is the drawback that it is tricky to get steam to condense quickly.
If you want to learn more about steam for aerostation, here's your man.
Given the waste heat available from the reactor, keeping the gas bags *toasty* would seem to be a good move.
The only move, if you are using hot air--"steamy" if you are using steam. The waste heat from these hypothetical reactors might be ideal for keeping steam vaporized.
Also, yet another traditional LTA buoyancy trick I forgot to mention is using "superheat" and "supercooling" to some advantage. The American naval airships would often try to time their flights so that the airship would pick up some extra heat from morning sunlight while the air was still cool, thus expanding their gas volume and gaining extra lift, which they would use to load on extra fuel, then as the temperatures of helium and air equalized, stay airborne on dynamic lift until they used up the extra fuel. There have been proposals--including by the Zeppelin works back when they were hoping to get helium for Hindenburg or Graf Zeppelin II--to artificially heat helium for extra launch lift. Any such maneuver, whether by natural or artificial means, lowers the pressure height until the gas cools again. In fact superheat is often the bane of any airship using helium--enough superheat can lower pressure height right to ground level, forcing that some helium be vented.
Uh, IMHO, the Zep' shape may not be the best shape, and a 'rounded rectangle' would provide more lift and cargo capacity for less structural weight. In effect, several skinny zeps', side by side within one envelope...
I really doubt this. Structurally, the ideal shape would be a sphere--minimum surface area to volume, and I don't think you can beat a sphere for static loadbearing efficiency either. Since a sphere is much more draggy than the elongated fish-shapes it isn't used, but the circular cross-section of the ellipsoidal ships is also hard to beat. I certainly don't think this proposal of yours is any improvement structurally; it clearly is a loser aerodynamically.
To be sure, minimizing drag is not quite everything; one might want better aerodynamic side forces, for dynamic lift or turning. You'd flatten it horizontally for the former, vertically for the latter. The "vertical airship" is yet another notion; the argument is that if the gas is kept in a symmetrical airfoil like a wing turned on its side, the structural forces are more in line with the load and so the structure can be lighter.
FWIW, putting vectored thrust pods on the corners would seem to give the best control moment...
Certainly at low airspeeds, yes. Better than the low to zero forces then available from the fin. But at high speeds they'd be quite inadequate, unless you are using such powerful thrusters one might ask why bother with static lift at all and just go for a flying bedstead!