How long have you had the snake? From you saying its your first feed then probably not long, believe me theres plently of time for that lamp to give you problems. Just because it hasnt happened YET doesnt mean it wont.
And i would not suggest just leaving him at your friends without a heat source.
Unless it stays 88 degrees in the house which i doubt
Give him the lamp at your friends until you get your rack setup with proper UTH and a thermostat
I would suggest waiting at least 3 days before you move the snake. If you just fed him, moving around alot can cause the snake to regurgitate and become stressed.