score:4
A quick google search revealed this tripadvisor review mentioning amazing brownies and air-conditioning, dating September 2014:
If you get the opportunity, call in for a coffee and a brownie in this air conditioned coffee shop. The cakes are all made on site, a large variety, but it would be hard to go past the brownie. Free wifi too.
Sounds like a perfect combination to me. The mentioned place should be here, according to google maps.
As a tip and trick I would suggest to try hotel/hostel bars. It would make sense to assume that the bar inside an air-conditioned establishment will also be air-conditioned. And often you don't need to be a hotel guest to use these facilities.