Not sure you've gave enough details, you should have told us the problem with the a/c and the type, this makes a huge difference...
but to answer the basic question is 100% yes you should pay something..
lets say you drove your car into my garage and went to drive away and it broke down, I would offer to fix it for you for a cost.
if you said no thanks, and asked is it ok to leave it here (inside of course its a classic car and made of wood) i would say yes no problem if its for a couple of days thats no problem.
if you then asked me to use my tools/space/car park etc etc.. and you want to wait and fix it your self once the parts arrive I would say you'd certainly be paying me something..
and why not you are using my garage which i pay rent/rates electricity etc..
then your parts arrive and you dont want to drive it home cause its raining
Jog On is what i'd say!!! pay up or park the sucker outside...
Now i'm a reasonable man and wouldn't take the *iss or actually leave someone high and dry like that,but if they took the *iss i'd leave there car outside, as its not my car why should i be responsible for it?
so unless you give us some more facts and figures we dont know if your being treated unfairly..
by the way..... can i come round and plug my caravan into your house for a few weeks to charge it up, get my fridge going and is it ok if i pop round after dark for a heat and a wee lie down lol!! pmsl!!