Tempers have flared pointlessly here, so let me do my best to provide a simple, hopefully helpful answer.
The hot end of a Peltier device is heated by the heat that gets pumped (by the device) from the cold end. When you apply power to the device, it heats the hot end by moving heat from the cold end, which is how the cold end gets cold.
So you don't want to heat the hot end; you want to cool it, presumably using a heatsink and maybe a fan.
For bonus points, we can take a lesson from the mechanical aircons and do this: The cold end is going to have water condense on it. You need to dispose of that water, of course, but what you can do with some of it is use it to wet down the heatsinks on the hot side so that evaporative cooling is added to the mix. On a typical window aircon, the equivalent takes place in that the condensate is collected in a reservoir (the excess is what drips out of the bottom of the machine) and the outside fan will usually have a ring on it that splashes this water up onto the condenser coil (which is the hot end and heatsink of a mechanical aircon).
In the end, I don't know if your Peltier aircon would be more efficient or not, compared to a mechanical one, but it could be a worthwhile experiment. Just don't heat the hot end, because that's getting the ideas wrong.