These are two very different issues. Raising the temperature to 86F/30C for two weeks will (or should) kill the ich and the fish will be fine. Increase surface disturbance via the filter which helps oxygen get into the water. I did this in my cory tank with some 50 wild caught cories including pandas and they were fine, and the ich killed.
As others also said, do not use medications for ich. Some do nothing, many will harm fish, some kill them. I can assure you that the rams and the cories will find ich-x way more stressful, and it might finish them off. The rams are already highly stressed or they would not have ich, so any additional unnecessary stress is a serious issue for them. And cories are quite intolerant in general of chemicals/preparations in the water. The heat is far less stressful; I have even had to use salt once, plus the heat, and the pandas and other cories got through that fine. Stress is the direct cause of 95% of disease in aquarium fish, so keeping it minimal is always better.
Going forward, you have to decide on what is best for the fish, and obviously removing the rams to their own warm space is what should be done here. Rams maintained below the 80F will never live their normal lifespan because of the effect of too low a temperature. And increasing temp for the other fish also weakens them because they are then literally working too hard to maintain ordinary life-essential processes.