This is an interesting theory, and I think that stormlight may in fact have something to do with temperature, at least with living Radiants.
When Kaladin used large amounts of Stormlight his clothes were coated with frost, and when he swore the Third Ideal the symbol of the Windrunners appeared behind him in frost. Then, when Lopen swore the Second Ideal the same thing happened.
The same also happened to Szeth when he swore himself to Dalinar, completing the Third Ideal.