I had the same problem as you in my 02 wrx.. except mine was climbing a 10% incline in the middle of wyoming summer =)
Anywho's.. the stock radiator cap and bottom are plastic. the plastic does wear out after a while and the weak spots do split and crack. IF that is your daily driver there is something you can do as a TEMPORARY fix. But i would reccomend parking it and waiting.
What i had to do because i live in seattle area and it was in wyoming that it happened. I found out that wire ties are the same material of plastic that is used in the radiator plastic. I was able to use a soddering iron to melt the plastic together and patch it up to get it home. definitely lower the radiator fluid level before hand otherwise you are heating it up and the fluid disperses it.
Once i got home though i parked my car and ordered a mishimoto radiator after reading reviews and talking to people on here.
I'd say yes to changing the belt as well because you will be removing a big part of whats in the way when trying to remove the belt. Now i'm assuming that you are talking about the timing belt right?