A dodgy aircon unit isn't a valid reason to withold payment of rent and if you do the landlord will be doing the suing. Antagonising the landlord is unnecessary and counterproductive. There's no need for a confrontation at this stage. Just write and ask firmly but politely for the problem to be fixed within a certain period of time. If nothing happens then get the 3 quotes, go with the cheapest and deduct from the last month's rent.