If your AC is constantly running and does not drop the temperature adequately it is undersized. If it is too cold and the unit does not shut off, the control that sets the temperature is not working correctly and should be replaced. It is an easy replacement. The advantage of a working factory control is it does not shut off the fan so the continual air circulation is helpful in maintaining an even temperature.
I think the Coolstat will do what a correctly working control should be doing, but it also will shut off the fan, if I understand its operation correctly. I have had to replace them over the years, but they tend to be pretty reliable so it has not been often. I am not sure whether any of the controls off the new remote control units could be swapped in, although I suspect it would be possible with some research on the schematics.
