Is my understanding of thermal energy correct? When I think of thermal energy I have always imagined that it some "wave" radiating off molecules (like light) but now it seems like heat is not radiating off molecules at all. Heres my understanding:
Molecule have thermal energy if they are vibrating. If a vibrating molecule hits another molecule moving less quickly, it causes it to speed up (I think of it like 2 cars- If one car is speeding towards a parked car then it makes the parked car go flying away). So, thermal energy isn't really a wave like light is-its just when molecules start moving fast.
Is this correct? And if it is then why is heat part of the electromagnetic spectrum? If this spectrum is defined as emitting electromagnetic waves then how is heat within this description?
 A: Yes, you can associate thermal energy with molecular vibrations. From a microscopic point of view, thermal energy is the internal energy of the system and from the kinetic theory we associate this internal energy to the temperature of the system and to its molecules' vibrations. 
On the other hand heat is any work the molecules of the neighborhood do on the molecules of the system that cannot (in the sense of practical purposes) be expressed by force times distance. For a microscopic system it is impossible to take into account every individual work on the molecules so we are forced to interpret these molecular works as heat.
Heat therefore is not part of the electromagnetic spectrum since it is an energy change, not electromagnetic radiation. The link between heat and the electromagnetic spectrum is in the fact that electromagnetic radiation interacts with matter and can cause vibrations. In particular, microwaves and mainly infra red radiation can excite the vibrational modes of molecules and thus they heats up matter. 
