I haven't searched for papers. I suspect that won't bear much fruit as both astronomical institutions I've previously worked for elected to go the empirical route, measuring and building their own quadratic temperature curves. So, I thought some "wisdom" of the last 2 years using the software I built might help. Take as much or as little as you like.

a. My focuser has tended to drift in counts over many months. This puts a bit of stress on new calculations of function slope, but definitely affects the offset (the b part of mx +b). Allowing users to adjust the offset while retaining the slope will allow for multiple instances of where adjustments are needed but the basic slope stays the same.
b. You'll need to factor both filter offsets, and different gear profiles. Filters should be "zero offset" relative if possible, otherwise things get complicated quickly.
c. The elevation residual data is pretty noisy (as you noticed), but there is a definite trend in there. You may want to allow disabling elevation residuals as an option.
d. I wrote an analysis function that looks at the log and calculates/fits a trendline function. I don't automatically enable this calculation, but rather report it for inspection. It's helpful, and people may (or may not) want to update the function based on the calculation. Sometimes, it's best to just see it but leave it be.
e. There are times during processing when it's important NOT to auto-seed the focuser. Auto adjust is good after a slew without manual adjust, but if manual adjust is done after the slew but before imaging, the manual start position should not be overridden.
f. I'm not sure if you're going to use a summing integrator or not, but I advise that route for multiple reasons.
It's going to take time and patience for users to characterize their gear. I put a warning in the log for instances when there aren't enough data points. It may be required to automate turning OFF auto adjustments until enough data is present to actually validate using the function. Otherwise, it could actually be worse!

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