Was talking about it the other day with someone who knows the show well. His version: The studio is actually kept at 55 degrees. Audience members are warned in advance so they can bring additional clothing.
Why 55? Apparently back in the 80s, Dave experimented with different temperatures on different shows. He tried 75 one day. 65 another day. The day he went with 55, jokes really hit and from then on that was the temperature.
There's even an article about the Letterman studio on the site of Multistack, the company that makes the theater's chillers.
Some folks say David Letterman doesn’t want to break into a sweat during intense interviews under hot studio lights. But, according to George Clarke, Theater and Building Engineer for CBS, the cool air makes the sound crisper and keeps the audience more alert. “Crowd reaction is very important in this business, and the comedy stays fresh in the cold, too” says Clarke...
At about 5 o’clock each week night, Clarke and his boss, Joe Soldano, Building Manager, must make sure that the temperature of the Ed Sullivan Theater is pulled down to 50° F before the audience arrives. The MULTISTACK chiller has never failed to cool things down. “The stagehands call this place ‘the refrigerator’.” In the filming rooms everyone sits around in winter coats, hats and gloves. They, too, are kept crisp and alert by the cool temperature.
Related: Comedy Feng Shui: 10 things that ruin comedy shows [Sandpaper Suit]