Cooler vs fridge

I have been using a regular cooler up until this point for all my trips, with pretty good success. However I am looking at making the investment into a fridge but I am a little lost in the size that I would need.

Right now I have a 62 quart cooler. But I know a lot of that space is taken up with ice that would not be present with a fridge. So what size fridge should I be looking at?

Also I keep my cooler in the bed of my truck under a tonneau and most of my trips are into utah desert or other hot climates, any suggestions on best bang for your buck fridge that could keep up with that?