I want to interpolate daily climate data available from 3 locations. I am not sure how to interpolate the data for daily values for 30 years from the available 3 locations.
See my answer at: Interpolation of Three Data Points
Rather than interpolating you should first wonder if that is a useful thing to do at all:
Would your map be better than using the average temperature for the whole area? Unless you know that there is a physical reason why temperature differences occur I would use the average value everywhere, and not make an interpolation. It may well be that the prediction is more accurate if you do that than if you use an interpolated map. Local differences may be causing the temperature changes rather than a large scale spatial trend.
What do you need the map for?
Where is your study area located? Are you sure you cannot get other data for the area?