What happens to cheese if I transport it in cold temperature (below 0°C, up to -20°C) for 5-7 hours?
What if it's at +10°C for 5-7 hours?
Can it go bad? If it does, do cool bags solve the issue of cheese going bad?
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:
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.
Assuming you are talking Celsius, your warmer temperature, +10 (I guess the +8 morphed into +10 between the title and the question), isn't really that warm. According to the website of the cheesemongers Paxton and Whitfield:
Some cheeses are best kept cool, others need a warmer environment; it depends on the type of cheese and its stage of maturity. Most hard cheeses that arrive with you will be fine at 8 degrees centigrade to 15 degrees centigrade, at warmer temperatures they will continue to mature; a cool, humid cellar would be perfect, or any unheated part of the house that has a constant temperature between 8 &15 degrees centigrade. Soft and blue cheeses need to be stored at low temperatures, preferably in a refrigerator between 5 & 8 degrees centigrade.
Even if others would disagree with them slightly, it doesn't seem like +10 is an outrageously warm temp. to transport for just 5-7 hours. I say don't worry about transportation at 10 degrees C.
Your other option, between freezing and -20, might not be as good. StillTasty recommends against freezing cheese. But as Catija suggests, it probably depends on the type of cheese.