In regression, is a higher adjusted R-Squared ALWAYS better?
Generally, a higher adj. R-square is better. In your case, you might be better off working on the representation of temperature in the model. It depends on the data, really, but you could try polynomials for temperature (squared term or so) or you could make „classes“. Plot temperature against y, to see if there is a non-linear trend in the data. If so, you need to try to represent this structure in your model, because OLS regression is parametric by definition.

Adjusted R-square balances the advantage of adding a new variable and the disadvantage of losing degrees of freedom. So in your case, the explanatory power of temperature seems to add little to your model. This may change if you change the representation of the variable, so that it better fits the data generating process. You need to try.