This is supposedly an image taken at a German WW II base in Russia of a heater cart being used to assist starting an Me 109.
This is a similar device being used in Alaska on a P-40 Warhawk.
As far as I know, pretty much every military during WW II had similar devices for use in cold weather climates.
The US employed literally thousands of the Type F1A utility heater that were used pretty much anywhere heated air was needed -- warming aircraft, tanks, and other vehicles or even supplying heating to barracks.
Essentially it was small gasoline engine that powered both the gasoline burner (similar to a modern torpedo heater, I believe) and also a fan that circulated air through a heat exchange chamber, not unlike a modern forced air furnace.
The one being used with the Warhawk may be an earlier version of the F1A.
As for building a literal fire under a tank engine, that was done, but only under the oil sump. Basically it was to warm and thin the oil.
More than once in years past did I do something similar with an old John Deere tractor -- basically built a small fire in a bucket and sat it under the sump.
The idea wasn't to let the flames actually lick the sump, it was to get a good solid bed of coals and a little active fire that would heat the oil sump without licking flames and soot up over the bottom of the engine.