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Check the wiring at the thermostat. If the leads on R & W are touching anywhere the furnace will run. That includes a short in the wall so the only way to rule that out is to disconnect R & W and see if the furnace still comes on. If the random turn ons continue or if they are too infrequent to disconnect the thermostat then replacing it is probably the best thin to do particularly if the thermostat is old.