I'll add 2¢ I guess. The readings done at distance will measure a circle of a particular diameter. That diameter will change depending of the design of the gun you are using. It is often a ratio, D:S Ratio. That means a 1'1 measures 1 inch circle at one inch distance. 4:1 at 4 inches it would measure 1 inch.
Accuracy is not dependant on distance at all it is dependant on the design of the gun they for the part are accurate to +/- 1ºC or 1.8ºF up or down. The emissivity is complicated and hard to explain simply so the simplified version is how much the gun reading is reflected. The typical general purpose gun is set up to be looking at brown paper. If you point at say the plastic of the tub the reading may be wildly inaccurate as it could read something else (your hand for example)
As for your question I would not hold 'point blank' but rather at about 3"-6 or so if you had say a PE1-2-3 you would be measuring an average surface temp of 3-6 inches Remember exactly perpendicular and a low reflectance and dark brown object for the most accurate readings. Personally I'll check a 4 in distance go in a bit and scan it over the same 4 inch circle (slowly scan) and average off the readings. And compare the two.
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