If you find some way to have a huge heat flow and if you can increase the voltage by orders of magnitude: maybe. In practice, probably not. LEDs need a minimal voltage (depending on the color, but at least ~2V) to work.
When I was a kid, there was a project in an encyclopedia that used a series of thermocouples to power a small radio. By
wiring thermocouples in series, you get what's termed a thermopile.
The design I read about used a lamp socket and candle along with a bunch of thermocouples.
Later I learned that Russians often used a similar arrangement to power radios.
Yes, LOL, you'll need a zillion thermocouples to make it from 1 degree C or F.
Piltier devices (used for 12 volt coolers) offer a simple means of getting voltage from a temperature difference.
I've applied 12 volts to one, allowed it to settle, and then used it to power a small 6v bulb for a short time. Fun!