I have a summer home in NJ. My wife and I had not been to the home for one month. The heating themostat was set at 60 degrees. When we arrived this weekend, the temperature in the home was over 100 degrees. The thermostat was absolutley blank and the heat was running. I changed the batteries in the thermostat and the reading was 03 and 04, indicating 103 or 104. I manually turned off the heat at the thermostate. Shouldn't the heater have turned off if the thermostat malfuntioned?

Not knowing what kind of furnace or tstat you have or model numbers it is/will be hard to help you

Thermostats are just switches, they have no inherent safety features, just off and on. If you were able to turn off the heat at the thermostat, your wiring is probably intact. Replace the thermostat. It will be cheaper than the fuel bill you will get for that one month.