LUT - Maximum error of linear interpolation approximation
The curve is smooth and monotonic, hence the maximum error is 0.5 degrees C. 

The derivative of the function will give you the slope, higher order derivatives are necessary to find the maximum error. You could fit a cubic spline (matching the slopes on either side of the area of interest) to the data points and evaluate the maximum error analytically, but frankly it would be a much better approach to simply evaluate at a much finer resolution than your desired accuracy, just as @Scott suggested in his comment 

Suppose you don't care about anything finer than 0.1°. You can easily evaluate over the entire range to 0.01 or 0.001 degrees C on a PC in seconds. The maximum error in those calculations will be +/- 0.005 or +/-0.0005 degrees C respectively, since the curve is smooth and monotonic at any resolution. 

Doing an simple brute-force exhaustive search will provide confidence on the maximum error. Unless your range is very narrow, or your ADC very fine resolution, you'll probably run into resolution errors with a typical thermistor long before you have unacceptable linearization errors.