[JRTJH]

If there is a wireless controller for the air conditioner, it's significantly more advanced than a "wired analog thermostat".... My guess is that if you can find the air conditioner/remote control set up instructions" somewhere in that document will be a procedure for changing the "set temperature tolerance". Older bi-metal thermostats ranged anywhere for +/- 5 degrees to +/- 3 degrees. Today's digital thermostats usually have a setting adjustment of either 2 degree or 1 degree swing.

If your "controller" is a remote system, I'd bet that there is a setting in the menu to adjust that temperature swing. The problem is finding the instructions on how to access and adjust it in the setup menu.....