I have a wall mounted Whirlpool air conditioner which was bought new 3 years ago. The thermostat on this unit appears to have quit functioning this summer. It just continuously pours out cold air and eventually causes the unit to ice up. Any suggestions as to what I can try to get the thermostat functioning once again?

I am sure the thermostat only controls a relay, not the power to the unit. The relay may be sticking. Relays are common, simple things having a coil that switches contacts. You may be able to find an exact replacement where parts for your brand of A/C is sold. Otherwise match the coil voltage, and contact voltage and amperage with a relay from Radio Shack or a hardware store and make it work.