What do you mean by "benefit"?  I have no scientific basis for my theory either, but I don't think you get muscular or cardiovascular benefits by running in the heat vs running in milder temperatures.  If that were true, I think gyms would be heated rather than air conditioned! 

I run in Georgia heat and humidity every summer and at the end of the summer I see no "benefits" from it.   I do run faster once the weather is cooler, but I consider that my base level.  Running in the heat is a handicap and once that handicap is removed I am running at my normal speeds again.  But I don't feel that I've gained extra fitness from running in the heat other than benefit of adapting to the heat and being able to tolerate it better as the summer goes on.

Galloway does say to slow down one minute per mile for every five degrees over 60. Which can get pretty slow if you don't run early in the AM.

Well, it seems logical to my lay-person brain that all things being equal (speed, distance) that if you're working harder due to the heat and it subsequently increases your heart rate that you'll burn more calories running in the heat.  I think it might be a little much, though to assume people keep the same pace at 92 degrees as at 65 degrees.

If being hot burned extra calories, then you would burn extra calories just sitting in a sauna.  Your heart rate will increase in order to cool itself while you are sitting there doing nothing.  If that burned extra calories and increased our fitness level, we wouldn't have to exercise at all! 

Sorry, I'm not buying it! 

I don't think the extra calories burned are significant.  Heat does make your heart beat faster, your veins dilate more and you breathe faster, just doesn't burn a whole bunch of calories.  I know people who do Bikram yoga, where the room is 105 degrees with 40% humidity, and eww.   I don't mind sweating, but that sounds so unpleasant.

So here is something I have to ask.

Would I get the same benefit by running in 10F weather than in 90F?

Dennis