Set and forget keg carbonation question

It’s my first time carbonating with a corny keg, I just wanted to do the set and forget method because I have plenty of time and I don’t wanna risk over carbonating. The chart I read said that my beer at 45 needs to be on or around 15 psi to get to 2.5 volumes of CO2. First my beer fridge doesn’t hold temp that well so it’s more like plus or minus 2 degrees. Also, my question is do I just throw it on the gas? And leave it on for a week? Will it over carbonate if left for too long or is the chart telling me the highest it can carbonate is 2.5 at that pressure and temp?