Usually people run them to a certain RH, relative humidity.
I'm not sure what temperature you're thinking (high or low) ... I leave mine on 24/7, it turns itself on/off based on humidify. I have it set for 65% which is about as good as I can get w/o it running almost constantly, and of course its duty cycle depends on outside conditions--if it's raining outside it will run more. If it's cool and dry it will run much less.
My basement isn't finished, but it will never cold enough to damage a running dehumidifer, if it does I've got bigger problems in the form of frozen pipes and congeled heating oil.
I have mine set at 60% RH, it cycles about every 2 hours, depending on weather. Newer models can run down to about 45 degrees F or so (so my manual says). But it should be nice n dry (and -20f) here before my basements gets below 55f.
hmmm, I've been a little curious about this too. I usually have mine at 65% as well because that seems like as low as I can go while still letting it switch on and off. Much lower and it's running near constantly which gets quite expensive.