For many speakers there is no difference between varmeco and temperaturo. If we follow PIV (and in this regard I do, at least I endeavor to), there is indeed a difference.

The confusion comes in over the meaning of eco and how it relates to terms in the various national languages. This is a broader question, but it's impossible to answer the original question without touching on it.

What is the difference, for example between varmo and varmeco? Between longo and longeco? Between eblo and ebleco? Between alto and alteco? It's tempting to translate these in our heads to warmth, length, possibility, and height - then jump to the conclusion that there is no difference. Indeed many very fluent speakers live their Esperanto lives for decades without noticing that there is a difference.

Look up these words in PIV and you'll begin to see the pattern. When we admire the longecon of a hare's ears, we're admiring how long they are. If we happen to like short ears, we would never say that we admire the longecon of a guinea pig's ears because a guinea pig's ears don't have longecon. We can say something nice about the longo of the guinea pig's ears, or even admire the mallongecon - but not the longecon.

Temperaturo is an indication of how hot or how cold something is.

is an indication of how hot or how cold something is. Varmo is the energy, or heat, that comes off of something warm.

is the energy, or heat, that comes off of something warm. Varmeco is the quality that a hot thing has.

I am not convinced that the pattern is followed 100% on all the -eco words. The general idea, though, is that if you are talking about the X-eco of something, you can usually turn around and say that this something is X-a.