Will a 75ohm cable work with (not break) a 50ohm gsm shield?
Your best choice for long runs of coaxial between 50Ω systems is really to use impedance matched cable with low loss. No-one is forcing you to use RG58 just because you need 50Ω! There's other cable types. What you want depends on frequency, (power is probably not too much of an issue here), weather resistancy, and cost – all three things that you'd probably have to answer by consulting a electronics distributor. GSM/GPRS sadly doesn't say whether it's 900 or 1800 MHz, and there's enough cable types that work well for the first, but not as well for the second frequency range.

Of course, low-loss microwave 50Ω cable might simply be prohibitively expensive. In that case: better lose a few dB to impedance mismatch at the antenna (not sure how you'll connect your GPRS device) than lose more dB in the cable. Notice that if you know the frequency, you can get/build an impedance matcher that will not be lossless, but pretty low-loss. Additional cost, complexity, and source of errors ensue.

But Andrew is absolutely right: Go analog as shortly as possible, digital for the rest. So, place your RF equipment close to the antenna. I'd rather switch a small current at the antenna which is used to actuate a relay that switches the heating 30m away (why, btw, are you using feet? I'd assume Norway has the good, non-freedom units of measurement?).

By the way, you're going through great lengths to get GSM into a remote location, just to switch a heating. 

Maybe that doesn't pay. I have positively no idea what a Iridium satellite pager IoT device costs. That might be a bit overkill, but would work as long as you're not bound to hide your antenna in a cave.

Another option might be to have your GSM/GPRS device close to the cell phone tower, and use another technology for the extremely low-rate communication with your home. That of course requires you can put up a GPRS device somewhere close to the tower, and add a transmitter for a different technology to it. I'm thinking about something like 433 MHz modules, which are heavily restricted in transmit power (much more severely than GSM phones!), but can be made to send long sequences at very low rates, which you could build a correlation receiver for at your house.