"Would you consider the linear motion of molecules as heat?
Dunno. Any physics majors in the crowd?"
I'm not a physics major. But liquids, gases, plasma, or solids traveling at high velocity aren't consider hotter or colder depending upon their velocity [though I have no comment regarding matter traveling near light speed].
In other words one could have gas at -200 C traveling at 1/2 the speed of light. Now, since there isn't a absolute vacuum any where, such a gas could impact other matter which could be travelling at a different speed, and therefore cause heat.
A gas or plasma is molecules traveling at a certain speed- it's definitional, solids and liquids aren't.
So, temperature is determined the wavelength radiation emitted from matter [see black body]. Temperature can also be determined the degree in which it heats some other object- such as thermometer [expansion or contraction of mercury inside a glass tube or a certain length of some metal].
In terms gas temperature there relation between pressure and temperature [see gas laws].
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