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Is it possible to calculate the temperature the heat source based on the temperature increase of the air a certain distance away?

I was thinking the inverse square law could be used because I had found sources online (like https://api.viglink.com/api/click?format=go&jsonp=vglnk_146248078578210&key=6afc78eea2339e9c047ab6748b0d37e7&libId=inurapry010009we000DAemnuf9u7&loc=https%3A%2F%2Fwww.physicsforums.com%2Fthreads%2Finverse-square-law-temperature-change-and-heat-source-temp.870235%2F&v=1&out=http%3A%2F%2Fm.nsa.gov%2Facademia%2F_files%2Fcollected_learning%2Fhigh_school%2Fstatistics%2Ftemp_distance_lab.pdf&ref=https%3A%2F%2Fwww.physicsforums.com%2Fforums%2Fgeneral-physics.111%2F&title=Inverse%20Square%20Law%2C%20Temperature%20Change%2C%20and%20Heat%20Source%20Temp%20%7C%20Physics%20Forums%20-%20The%20Fusion%20of%20Science%20and%20Community&txt=This%20classroom%20experiment) saying that the temperature increase an object experiences from thermal radiation is subject to the inverse square law.

I was thinking that, if the air, say 4000 radii away (heat source ~ 4 m, area of effect based on size of storm alone has radius of no less than 17,000 m), experienced a temperature increase of 10 K, the temperature of the heat source would be

(4000^2) * 10 K = 160,000,000 K

or (assuming the air starts off at 25 degrees C = 298 K)

(4000^2) * (298 K + 10 K) = (4000^2) * 308 K ~ 5,000,000,000 K.

Am I completely off here? I focused on heat transfer through radiation because I've read that radiation takes over as the dominant form of heat transfer with high enough temperature differences. Would it take a temperature of 100,000,000+ degrees to heat the atmosphere from so far away? (I know a temperature like this would do far more than simply heat the air in real life.)