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Your house thermostat most likely is rated for 24volts or may even 12volts. It works by activating a relay to power the heating/cooling parts of you home heating system, which would be a high voltage setup. This type of thermostat could be made to work with a incubator, but would require a seperate power supply for the thermostat, as well as a relay to supply the higher voltage for the heating strip.
Further, most home type thermostats are simply not very accurate and usually have a very high hysteresis, (hysteresis is the amount of time between the off and on cycle of the thermostat). One reason for this is simply because of the type of temperature sensor used in making the thermostat. Most home thermostats use a very inexpensive sensor. The digital thermostat works by sending electric signals to the computerchip located on the circuit board inside the digital thermostat. The computer chip interpets these signals as a increase or decrease in temperature. The more precise the signals, the more accurate the actual temperature reading.
Just keep in mind that analog to digital conversion is the more precise the higher the bits are. Keeping in mind that analog to digital conversion depends on the bits to convert to the number is the exponentional value for conversion, e.g. at 8-bit the maximum (finest) resolution is 2 to the power of 8 equalling 256 different values for the span you intend to convert. Assuming temperature conversion of 0 to 100 deg the finest resolution you can get using 8bit conversion is 100/256 (approximately 0.4 degrees) 12bit conversion means 2 to the power of 12, which is already 4,096. Using that value for the finest resolution the best accuracy would already be 0.0244 degrees per bit. A 16bit conversion would mean 16,384 possible values, leading to an accuracy of 0.006 degrees. Most of the homeowner type thermostats are only accurate to +/-2degrees or more. This variation of accuracy increases the lenght of time it takes the thermostat to turn off/on and can result in an extreme overshoot or undershoot of the desired temperature range.
Sorry Walkswithdog, I know what you are going to say, but I just had to do it
As long as you obviously understand that you are a bad man, it's all good