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I am looking for some kind of software (free software) that allows me to make an interpolation like PRISM software.

The interpolation used in PRISM is a

local regression and accounts for spatially varying elevation relationships; also accounts for effectiveness of terrain as barriers, terrain-induced climate transitions, cold air drainage and inversions, and coastal effects

What I am aiming to interpolate are climate time-series datasets.

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PRISM is highly specialized. It is maintained by a group that appears dedicated to providing its output but not the software itself, which is evolving. Therefore I doubt you will find anything like this in free software unless you can get the original (or can port the source of the original, which started out as an ArcView 3 application). These researchers do invite interested parties to contact them: visit prism.oregonstate.edu/about_us.phtml. – whuber♦ Feb 23 '12 at 16:58

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Given you've tagged R in your question I'd take a look at the CRAN Spatial View and the gstat package in particular. Not sure if it has the exact PRISM interpolation method, but it would certainly be a good place to start.

Alternately you could look into the SciPy interpolation and ndimage subpackages if you'd prefer to work in Python.

Good luck!

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