I would like to see the difference of including DEM in interpolation from without. Some studies on climate data interpolation suggest that interpolation performs better with DEM. How do I do this in ArcGIS 10.2?
Search for regression kriging or kriging with external drift.
But on topic: How many datapoints do you have? What exactly do you want to predict at which scale? Kriging and especially regression kriging need a large number of points (definitely >50). I have seen more studies where kriging is abused than where it is used correctly. It may be better to do some exploratory data analysis first before jumping to an interpolation method. Perhaps there is a map with climate zones already which may perform better than kriging/...?