I think the problem is that your fridge, when given power, will always try getting you to your set temp. If your max temp on the built in thermostat is 45, when your timer reapplies power, it's going to start working on dropping it to 45. If I understand your theory, if you time it just right, you'll only give it enough on time to get down to say 55dF. It will be tricky because your outside temp may not be consistent and any tendancy to rise or fall in temp will be somewhat additive so your actual temp may snowball out of your expected range.
I wonder what it would take to modify the temp range of a stock controller. Maybe it's a simple resistor value change? I have no idea what kind of circuits they're based on.