You have a bit of a skewered idea on why a different line of thought appears in science, and in physics in particular.
If you look at Einstein and the history of physics, he came up with the idea of Special Relativity not because he was bored and decided "Hey, what if...?" out of nowhere. There was a very clear impetus for him coming up with the idea because of the problems of Maxwell equations not be covariant under Galilean transformation. In other words, there was a problem at that time, and he was trying to approach it from a different perspective. And then, when he came up with a new idea, he did one very important thing. He showed mathematically that this new idea converges with the old description.
Unfortunately, you never gave a clear impetus for why you'd want to think of temperature having the same "relative" concept. You simply can't invoke "Well, what if... since we already have relativity...", without specifying what exactly is the problem that would be solved if we look at thermodynamics from the different perspective. In other words, what is the worth of our time to delve into this? What does it do? What does it solve? Can it clean windows in record time?
There are infinite number of ideas out there that one can explore. The question is, while it may be interesting, but is it important? Those two criteria are not necessarily mutually inclusive.
Zz.