CRJ-200 Captain reported smoke in the cockpit during departure taxi which prompted the flight crew to requested priority handling to return to their gate. Airport support personnel and maintenance met the flight at the gate. After maintenance MELed the pack issue the flight departed safely.

Narrative

While taxiing from gate to [the] runway; noticed a smell in the flight deck. While holding short I looked right and noticed smoke coming from the right side of the cockpit. We had no Engine Indicating and Crew Alerting System indications. I told the First Officer we have smoke in the cockpit tell Ground we need to return to the gate now. Ground replied standby. I said [request priority] and ask for fire equipment and that we need to return now. Then they advised us to taxi back to the gate. While I was taxiing back the gate the First Officer looked at the systems pages and noticed the left PAC temp was white and indicating 120C he turned the left PAC off.While taxiing I asked him to ask the Flight Attendant if there was smoke in the cabin. She said no. As we approached the gate the smoke had subsided. It is for those two reasons I decided to leave the Passengers on the aircraft. The Flight Attendant opened the door. She then advised there was a smell and just a little smoke. Only a pick-up truck style fire truck showed up; someone then came into the jet ridge asked if we were okay; we said yes and they left. I made an announcement to the passengers that we isolated the problem and that we are going to hook up the jet ridge and de plane normally. Which is what we did.Called local Maintenance; then called Dispatch; then got connected to Maintenance Control. Called Dispatch back and asked to talk with the duty Captain. Explained all to him. Went to the gate and made a podium announcement to the passengers explaining what happened. After Maintenance had fixed (MELed) the problem; I made another podium announcement again explaining what happened and the resolution and that we would re-board. After boarding I made another announcement from the front of the aircraft with the flight time and thanking them for their patience. We departed and completed the flight to ZZZ. After talking to maintenance; it was determined a heat sensor had failed.