Ghost,
Good observations. Yes, c has the greatest sensitivity. Sometimes it's possible to get a better fit by massaging the inputs to the fit mathematically. In this case, you could take the natural logarithm of the output data if you're very sure in your measurement accuracy of ψ. Then you're fitting:
which could be much better behaved because its inputs are an inverse term, a slope, and an intercept. Depending on the range of the data and how linear it appears, a could still be negligible, or it could be substantial. In this form you've got one term proportional to T, one that is inversely proportional to T, and a third one that sets the offset of the whole function, which might work pretty nice!
Again to hammer back on the measurement accuracy, by taking the logarithm, you're de-emphazing some of the variation across the output points to tease out some clearer behavior of the inputs. It's possible that the constants you obtain will be less effective against new data for the fitted curve -- it's always helpful to have a few extra points that don't contribute to the fit to test out its validity.
(Edit: Sign error)
