When you add energy input to a system, it doesn't immediately reach its new equilibrium temperature. That's not an analogy, it's another example of the same physical process.
That's an analogy.
But it is better to say that experimental physics is based on the collection of data about a particular phenomenon, and fitting those data to mathematical models to test how well their predictions hold. And that is not analogy.
technically analogy has a broad definition that applies anytime you compare two things.