Let me see if I can pick apart your misconceptions.
About the flywheel example, no, rotation does not lead to temperature, because the rotational energy of the flywheel is not thermal energy. You seem to be mixing up thermal with non-thermal energy. In thermodynamics we assign several different kinds of energy to a system:
But here's the kicker: The division between these concepts is not a fundamental law of nature, but depends on your model. So yes, you could build a model where rotation is included in thermal energy. But then, rotation would be part of the entropy as well, so at nonzero temperature you could not model it as rotating at a fixed speed! You'd have to model the rotation as a random variable. Clearly this contradicts with rotation at a fixed speed. That is, unless you also set the temperature to 0 K, in which entropy would be zero and so you could set the rotation to a fixed speed.
Now about the relationship between internal energy and degrees of freedom. You're misunderstanding what a degree of freedom is. The equipartition theorem says that the average energy of a particle with n degrees of freedom is nkT/2, but even if you included rotational energy as thermal energy, a large spinning object has much more than one degree of freedom. It has degrees of freedom associated with its many vibrational modes. It has so many vibrational modes that the associated 'temperature' is actually very low, not high as you describe. Indeed, if it were to 'thermalize' (say, through friction), it would not warm up the object that much. If it were true that the temperature due to rotation is 1e22, then if you let it thermalize it would violate conservation of energy, by tens of orders of magnitude (it would turn into quark-gluon plasma and explode violently, vaporizing half of the planet Earth).
And finally, you cannot calculate absolute energy for an object moving linearly through space. The kinetic energy depends on the rest frame.
Let me see if I can pick apart your misconceptions.
Ok, I have a PhD in Applied Physics. I have learned thermo and statistical mechanics a few times including two graduate level courses. I have recently been analyzing internal and external combustion engines as part of my job, and have relearned some parts of thermo for that. It may be that despite my background, I have not done a good job of explaining what is going on with thermo. But what I am explaining here is, at worst, the way a working physicist would see thermo, informed by a science that ex...
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