Yep, a good cleaning is needed. But while you're at it check the solder joints for grins and giggles.
When most material heats up, it expands. In the case of pots, the sliding contact can make better contact with the resistive strip, might become better at pushing the dust out of the way, or the resistive strip could close a small crack, etc. etc.
I once had a fender fuzz-wah pedal. It wouldn't work at all cold, but when it warmed up to room temperature it worked great. I eventually took it apart and after days of searching found a bad solder joint on a resistor. A little bit of new solder and it worked cold again. The expansion of the metal when warm enough made the connection, then broke it when it contracted due to the cold.
