Similar work i have done in Arc/GIS. see below link

http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=An_overview_of_the_Interpolation_tools

Try KRIGING

http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=Kriging

You can apply  the inerpolation methods (Radial Basis Function and Kriging) then you can compare the accuracy of each method .

The inerpolation methods will be applied according to the rainfall rate field for  spatial analysis of rainfall and the temperature values and distributions fields for spatial pattern of temperature.

For temperature, at least, there's strong correlation of this variable with laltitude, latitude and longitude. If you have access to meteorological data, you could interpolate temperature using a multivariate regression using LAT, LONG and ALT as independent variables and estimating temperature. It's not interpolation per se, but I would argue that it could be more accurate than interpolated values and has the advantage of not requiring to estimate interpolation parameter (or let the software estimate for you).

In the end, you would have a daily (or whatever is your temporal scale) model looking like:

Tlat_i, long_i, alt_i = a + lat_i * b + long_i * c + alt_i * d

And latitude, longitude and altitude are easily obtainable. If you doing a map, you then would need to calculate the T for each node in the grid, or pixel in the image, which is also straightforward.

Rainfall, on the other hand, is a nightmare. I'm not aware of any simple method for interpolate it or estimate it reliably.