How long should I keep a lambic at fermentation temperature?

Normally I ferment beer in my basement, which varies in temperature from 50-70 degrees, depending on the season. These temperature swings can be bad for fermentation, especially in winter. So when I brew ales, I use a heater + temperature controller to keep the beer at fermentation temperature for the 5-10 days it takes an ale to finish.

Soon I plan on making a lambic, which will stay in the carboy for several months, if not years. Do I need to keep the carboy at fermentation temp for the entire time the beer is in there? Or should I just keep it warm for the first week or two, then let the brett do its work at ambient temperature (which will be 50-60, as we're heading into winter).