Disconnect the power to the Honeywell mercury thermostat by turning off the breaker or removing the fuse.
Pull the cover off the front of the thermostat. Remove the two retaining screws holding the thermostat to the junction box with the Phillips screwdriver. Pull the thermostat out of the box, exposing the wires.
Unscrew the wire nuts connecting the mercury thermostat to the wiring in the junction box. Remove the thermostat.
Connect the white wire going to the heater to the red wire marker "Load" on the digital thermostat. Connect the black wire going to the heater to the black "Load" wire.
Connect the remaining black wire from the thermostat to the black wire from the service panel. Connect the last white wire from the service panel to the red wire from the digital thermostat.
Place wire nuts on all connections and tuck the wires into the junction box. Place the digital thermostat in the box, insert the retaining screws and tighten.
Replace the fuse or turn on the breaker to restore power to the thermostat.