This quote is from Endkampf: Soldiers, Civilians, and the Death of the Third Reich by Stephen G. Fritz, it is referring to battles for Aschaffenburg, Crailsheim, Heilbron, Nuremberg, etc. because it is talking about the region 'bounded by the Main and Neckar Rivers'. A source btw that in consecutive paragraphs starts speculating as to how many German army deaths there were at Nuremberg (note the word 'likely' is used to describe this denoting they are making it up). Anyways it says nothing about casualties for Heilbron, specifically.
And if this is the part of the article you are referring to in the last link
Seems clear to me that the author has no clue what they are talking about and are just speculating because they cannot even decide if it is as many as US losses or 'many more'.
Roberto Muehlenkamp seems to contrive figures for German and US army losses.