Not only would it be possible, but there already exists one (http://clearclimatecode.org/) which has recreated GISTEMP in Python, found some bugs, but find that their code produces near-identical results to original GISTEMP. They say:

It is our opinion that the GISTEMP code performs substantially as documented in Hansen, J.E., and S. Lebedeff, 1987: Global trends of measured surface air temperature. J. Geophys. Res., 92, 13345-13372., the GISTEMP documentation, and other papers describing updates to the procedure.

This ccc-gistemp project seems, however, to be stalled, in that it hasn't released anything since 2010 (though there were a few blog posts in 2011). This doesn't seem to be because they achieved everything they hoped to; the last information on their website indicates that there's plenty more to do.

(This was made possible not because anyone leaked or stole anything, but because NASA released the GISTEMP code.)