Air carrier Captain reported the cockpit inflight temperature gradually became colder to the point where only cold air was available. The flight crew diverted and was unable to reproduce the anomaly on the ground.

Narrative

On Day 0 at approximately XA00z we were at FL390 in cruise. The cockpit temperature had gradually been decreasing from 24C when I first noticed the cold temperature. I began to incrementally increase the temperature control knob but did not notice any increase in temperature. When the cockpit temperature began to display 21C we received the Flight Deck Temp EICAS message. A few moments later the EICAS message cleared and I began running the QRH procedure for Cabin Temperature Cold. I was running the checklist and letting the clock run to approximately 90 seconds when described before proceeding to the next step. After completing step 11 and 12 an odor of smoke and visible smoke began filling into the cockpit. I undid step 11 and 12 and we could tell smoke was no longer filling into the cockpit and began dissipating. At this point the temperature in the cockpit was indicating 19C and the outlets were only able to produce cold air. After discussing options and further review of the QRH we choose to start a descent and divert to ZZZ with was approximately 100 miles in front of us. Company Dispatch was advised of our situation and alerted ZZZ ops and Maintenance. During the descent there was no longer any visible smoke and only a slight odor of smoke/fumes. It was decided that it was not needed to don our Oxygen masks but if the smoke and fumes returned they would be donned immediately. A visual approach was completed to Runway XXL without any issue. It should be noted that we did not declare an emergency or request priority handling. Some type of mechanical malfunction. After arriving into ZZZ we conducted a test of both Left and Right PACKS and were unable to duplicate the issue. We than conducted and idle engine run while parked at the Gate and still were unable to duplicate the issue.