Most appropriate weights for interpolating temperature for a point from raster data

I have raster data for minimum and maximum temperature from NOAA’s CPC Global Daily Temperature data set found here https://psl.noaa.gov/data/gridded/data.cpc.globaltemp.html

I also have survey data, which includes GPS/date information. When I merge the temperature data from the raster file into the survey data set, some of the temperature data is missing for coastal cities. NOAA only interpolates land squares, and not water squares, so some squares on the coast are mostly water and not interpolated.

My solution is to take an average of the temperatures of the adjacent non-missing squares weighted by the distance from their center to the GPS coordinates of the survey site.

What sort of weight is typical to use for interpolating temperature data? I’m currently using inverse-squared, but wondering if a linear approximation is better for temperature?

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Update in case anyone else ever sees this post…

Since I didn’t hear back, I did some regression analysis for different types of weights. I imputed temperature for survey sites that fell into raster squares I had data for as the average of the 8 adjacent squares using inverse distance weights, inverse-squared weights and weighting the closest square 100%. I then regressed the non-missing data on the imputed temperature data for each model. I also varied the regressions by starting with all available data, and then gradually dropping observations with more non-missing surrounding raster squares. I found that the linear weights worked best for all data (mostly inland squares) while the "closest square" weight worked best for observations with 4 or fewer non-missing adjacent squares (presumably the coastal squares). The inverse-square distance weight were a close second at both extremes of the analysis, so I decided to go with that.