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There are several issues here that you should be aware of.
The cooling systems (unit that sits outside) is not designed to run in cooling mode when it is much below 70 or 72F outside... running in cooling mode, when it is also cool outside, and *especially if you set the thermostat below 70F.. will cause the indoor cooling coil to freeze, often encased in a 20 pound block of ice... that blocks the air flow and of course prevents further cooling... and is bad for the cooling unit compressor outside.
There are however solutions for all of this... but those will most likely have to be added to your system. Those are a condenser fan cycling device called a 'head pressure control'... and an adjustable low pressure cut out control.. that can be set to defrost the indoor coil.
Regarding over-riding the outside temperature control....that outside air temperature sensor is connected with two wires.
If you unplug the sensor where it connects outside, it will bypass either the heating or the cooling limit functions. I do not know which.
So, unplug it. Then if you find it allows you to run the system as cold as you want to, you are done. You have accomplished your goal.
However if you find now that cooling will not come on leave it unplugged and fit a jumper wire across the the two female sockets at that unplugged molex connector. (Or you can do it where there those two wires connect inside your controls system.)
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