As New York braces for another sweaty, subway-platform-melting summer, the state is once again handing out free air conditioners to eligible residents — because surviving July without one is basically an Olympic sport. Applications for New York’s Cooling Assistance Benefit opened April 15, offering qualifying households a free air conditioner or fan, plus installation, just in time for the season when apartment living starts to feel like slow-roasting in a brick oven. The state-funded program, part of the Home Energy Assistance Program (HEAP), covers the purchase of one cooling unit per household — and yes, they’ll even haul away your old clunker if needed. For window, portable A/C units or fans, the benefit covers up to $800, including installation. Existing wall sleeve units can be covered up to $1,000.  Minor repairs needed to safely install the unit are also included, sparing New Yorkers from yet another wallet-draining summer expense.…