Furnace Thermostat Wiring Issue

On our spring break trip earlier this year our furnace stopped working. Turned out to be the wiring to the thermostat. It started as 2 strand wire, but mysteriously exited the ceiling as 3 strand wire to the thermostat. Why does it start 2 strand and end 3? Who knows!  I assume the splice failed, but because it runs through the ceiling it was impossible to pull.  I'm not sure why it runs up the aft end of the bathroom, through the ceiling, then down to the thermostat anyway, since the shorter run is below the shower pan. Which is the way the power for the bathroom light is run, to the switch which is located right next to the thermostat!