I think Hoover would have followed the traditional two-term limit that FDR broke. Therefore, a Democrat probably still would have been elected President in 1940, assuming Hoover is re-elected for a second term as the economy slowly recovers (which it did during FDR's second term).
Who? Well, some possibilities might be:
John Nance Gardner, FDR's VP in OTL
Cordell Hull
Note: Hoover's VP, Charles Curtis, would have died in office had Hoover been re-elected in 1936. If Hoover decided not to run for a third term, the Republican nomination in 1940 might have been wide open.