If you mixed your chemicals downstairs at 70F and took them upstairs where they slowly cooled down to 60F (for example), you might see the time for the image to appear get longer over the course of the session. But I wouldn't think you'd need to increase your light exposure time (assuming you don't have a lot of variation in the negatives you are printing from).

Does the Beseler use a halogen bulb? I once had an extremely frustrating session where it turned out the output of my enlarger bulb was dropping as it was on the verge of dying, but it was still putting out some light and at f/8 I couldn't really see the problem with my eyes.