Let's put it this way - I can come into the room and see my cat's footprints on the floor 15 minutes after she wandered through.
The battery will cool off but as anyone who's tried to charge one immediately after a flight can attest it takes quite some time. Then there's usually a thermal disparity between earth temperature and air - assuming it made it to the ground
It's a tool and as such not always applicable to every occasion - like if you drop it into a pond, or it falls behind something large enough to obscure the thermal signature. Tell ya what I'll fly later today and take some images after the flight and then 30 minutes after. I never did that so maybe I'm over optimistic on the thermal mass of the battery and drone body. The software constantly adjusts the image colors to accommodate the detected thermal gradient. That's how it can show the cat prints so long after. It's really a useful tool - I originally got it to evaluate home improvements and detect leaks. It worked beautifully for that.
Thermal Cameras for your Smartphone