How to measure the temperature of a fridge with arduino?
Probably the easiest way to do this is using a thermistor to measure the temperature directly. Since you don't want to put a wire inside the fridge, you'll have to find some way to interface the arduino with the existing fridge electronics. I can't tell you how exactly to do this, because every fridge is going to be different. The easiest way is if the fridge already has a built-in warning light for high temperature. Connect a digital input pin to detect when the light is on. If the circuitry is hidden, you could also use a photoresistor to detect when the light comes on. Interfacing directly with a microcontroller or LCD will be very difficult. At that point you are better off just putting a wire inside the fridge.