The kegs have to be carbed properly which means they should be chilled during the carbonation process. I've let the kegs warm up to room temp with no issues. Sometimes it's unavoidable when setting up for a big event, or if you take it camping with you. I'm sure if the beer were served...
The kegs are pre carbed and ideally pre chilled but it's not necessary. I've served from room temperature kegs before with no problems. 50 feet of coil submerged in ice is enough to chill the beer on its way out.
4 years ago I built a wooden jockey box:
https://www.homebrewtalk.com/showthread.php?t=428860
A friend from my homebrew club likes to point out that it's the #1 result when doing a Google image search for "wooden jockey box". Quite an achievement! I'm hoping to bump it to #2 with my new one...