Hello,
Such icy, hot feeling sensation of the penis can be due to anxiety,contact dermatitis,traumatic damage to the nerves of penis, diabetes, prostatitis,genital herpes,urethritis and STD’s like Gonorrhea and Syphilis but they are less likely in your case.
I would suggest you to keep the area clean and wear cotton underwears.Also apply a mild steroid cream on the penis. If the symptoms persist then the above said conditions have to be ruled out. Please consult a urologist in that case.
I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
I had similar feeling in spine in the winter and in other seasons I used to get my feet hot. No diagnosis could be arrived at.