What happens to cheese below 0°C and above +8°C?
Though my answer won't go into the "technical" side of things as Lorel C.'s answer, I can answer from experience.

I regularly travel to The Netherlands and when coming back I'll always bring cheese back with me on the flight. (Flight duration ~4,5-5 hours)
I've brought back all kinds of cheeses, last time I brought a block of yellow Gouda cheese, block of Danablu cheese and 2 kinds of parmesan cheeses.
I've never noticed any tangible difference in quality of the cheeses after travelling and they stay good for at least the stated shelf life of the cheese.

What I tend to do is:


Make sure the cheeses are vacuum packed.


Helps store the cheese and ensure if any fats dissolve from the cheese they don't ruin anything in my suitcase.

Wrap them in bubble wrap.


I find this to be more flexible a packaging compared to a coolbag and as a bonus it doesn't add much extra weight.

Keep the cheese for as long as possible in the fridge before the flight.


I.e. put them in your suitcase just before you leave to the airport, but do make sure you left enough space for them :)



I personally haven't tried freezing the cheese as I'm worried that would ruin the cheese so I can't quote experience on that.