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I have MODIS satellite imagery that depicts a range of surface temperatures. However, many of the cells are missing values. I think I need to perform Kriging in order to obtain an average value for the empty cells based on the values of the surrounding cells. I'm not sure how to do this because I'm working with raster data.

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If you want the average value, then you could use a mean filter (focal statistics, ignoring the NoData value). This will be way faster than kriging, and it will work directly from a raster.

Then you use the raster calculator to replace the nodata values with the mean values :

Con(Isnull("input_raster"), "smoothed_raster", "input_raster")

As a remark, ArcGIS does not have kriging from a raster, so you would need to do "raster to point first"

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