Two bodies, one hot and one cold, are kept in vacuum. what will happen to the temperature of the hot body after some time?

There are two possibilities:

According to 1st possibility :

If the bodies are in touch then the temperature of hot body decreases and the temperature of cold body increases due to heat transfer and at a point the temperature of two bodies becomes equal.

According to 2nd possibility:

There will not be change in the temperature of two bodies. There will not heat transfer here.

Note: Heat transfers from hot body to cold body.

Hope it helps :)