"Illuminant" is a word describes an object sending out light, is there a word to describe an object sending out heat? Thank you.?

Thermal or radiant.

Well, there are three ways heat can be transferred, conduction, radiation and convection.
If by "sending out heat", you simply mean have heat be transferred from inside the object to outside the object, then the word you're looking for is "heating".

If by "sending out heat", you're talking about a contactless process by which thermodynamic energy is "cast" out of the object, then radiation is the only of the three ways that corresponds. Light is a radiation and carries energy so something that shines also sends out heat.
For something that emits radiations, the word you're looking for is "radiating".