Actually you can freeze cheese! We buy a wonderful cheddar from our farmers market that the maker says is fine to freeze - handy b/c she sells it in quite large wheels and much as I love it, 2 of us can't eat it fast enough. Depending upon the cheese, you'll get mixed results. I have read that if you freeze monterrey jack, it may become a bit grainy, but if you are melting it, that may not matter at all. I found this online:
TIPS FOR FREEZING CHEESES:
Freeze pieces of a half-pound or less.
Use moisture-proof and airtight wrapping.
Freeze quickly and store at 0 °F for two to six months.
Thaw in refrigerator so cheese won’t lose moisture; the slower the cheese is thawed, the better.
Use as soon as possible after thawing.
***So I'd suggest you try it with a small piece and see how you get on!