In a narrow sense: synonym for infrared radiation.
In a more general sense: The electromagnetic radiation emitted by every body with non-zero temperature due to the laws of thermodynamics. The properties of this radiation (in particular: its spectrum) depend on the body’s temperature – in the simplest case, that of what is called a blackbody, they even depend on nothing but the temperature and some universal constants.
For everyday temperatures, such as those of a hotplate, thermal radiation is emitted mainly in the form of infrared radiation. At higher temperatures, significant amounts of visible light are emitted, as well: a hotplate that is very hot indeed looks dark red or even light red; molten metal looks yellow or even white. In more extreme situations, thermal radiation can have energies that are even higher – for instance, the gases in the accretion discs of black holes are so hot that they emit great amounts of thermal radiation in the x-ray region.