This is just your skin starting to sweat. I complained about this to an extremely fit friend and his somewhat disdainful advice was that I needed to exercise more. Perhaps this answer is not at the level of rigor you wanted, but I think everyone experiences this, and the more you sweat, the less uncomfortable sweating becomes.

I'd like to tack on to this question by asking about itching and the onset of sleeping. Someone I know has a serious enough problem of getting very itchy right before sleeping, to the point of not being able to sleep. My first guess was dust mites, but freshly laundered sheets do not stop the itching, and no itching occurs when wearing days old jeans.

For a while I've had mysteriously itchy skin which seems triggered by hot showers, temperature changes, and time-of-day. I was told antihistamine tablets (sold over-the-counter for hay-fever) can help, but I have haven't tried it yet.

(Another common cause of itchy skin is being too dry => apply moisturizing lotion twice daily. It doesn't sound like what you have, but I guess you could try).