You are dealing with several symptoms and to really understand it might take some research.
1. the temperature sensor (thermostat) is usually located on interior wall.
Meaning in 110F outdoor heat- the wall with sensor might be 68, but exterior wall can be 80F or even >100F.
In 0F outside cold the same 68F internal wall will be paired with external wall at 30-50F while temperatures between the walls will wary.
2. the thermostat switch has cut-in and cut-out temperatures.
For AC you set cut out at 68, but cut in will be about 72F,
The same setting in heating mode will cut-in at 65F