An animal warming up in the sun is gaining heat via

The answer is radiation.

There are 3 types of heat trasfer. Convection, conduction, and radiation.

Convection is not possible since the space is vacuum. There's no fluid to circulate.

Conduction is also not possible because vacuum is the worst thermal conductor, it doesnt conduct heat at all.

And for radiation, it is the flow of electromagnetic waves. It can occur under vacuum state which makes it possible. The sun is a net emitter because it has a higher temperature than surroundings.