Geometric weighting of temperature
It sounds like you're describing optimal interpolation (AKA Gauss-Markov analysis, objective analysis, probably others too). This is a solid intro, and this is a powerpoint on the subject. It's a hard process to summarize quickly, but roughly speaking, you're on the right track.

Optimal interpolation is fairly common in meteorology and other environmental sciences, but I'm not convinced it's really the best tool for the job. Any statisticians want to take a crack at it?