Signification of variance and error in "krige" and "krige.cv"

I obtain some interesting results.  For example, the variance from
"krige" is around 24 and 40 (mm?  same unit as the raw variable?),

If it is a variance, then it is obviously in mm?.

So, is it normal that the variance is so high?
Does it mean that the interpolation that I did have a major flaw?

Estimation variance only depends on data points and variogram (or
covariance) model that you have chosen. It is of course 0 in the data
points (check this in particular), increases with the distance from
the nearest data point. Maximum of this estimation error should be
comparable to the population's variance (or the sill of the variogram,
if it has one).

Now: which variogram model did you use? A linear one? Have you got the
same amount of data for the temperature and for the precipitation?
Anyway: such variance is not so big. You should standardize it on the
stdev of your data to convince yourself. The fact that estimation
variance for the temperature is so low, is due to its low variability
(range: 26-29, as I understand from your mail), and *that* is
particular, not the wider range for the estimation variance of
precipitation.
I hope I answered your questions, regards

ScionForbai