I was recently on a flight from SXM which didn't have air conditioning for the first hour. The vents were blowing very hot air which made it even worse. The captain finally came on and said the air conditioning was broken due to the high heat and humidity from being on the ground in SXM, but they were working with maintenance to solve the problem. The FAs asked the passengers to close all of the shades and vents until the A/C came back on. I was wondering if they would turn the plane around if it didn't come back on. (This was a 5 hour UA flight from SXM to ORD.)