it depends of the distribution of the data. If the data are normally distributed you have to use parametric statistics, by the other hand, if the distribution isn´t normal, you have to use no-parametric statistics
it is often best to fit first a regression with temperature (and possibly also including moisture). The fitted parameters can then be compared. Many studies have been done on this. Check for example work by Jorge Curiel-Yuste, Ivan Janssens, Michael Bahn, Iain Hartley, Andreas Heinemeyer, myself, ...