Does this fixture need a certain room temperature to work properly?

I would follow the manufacturer's suggestion. I've heard of many florescent lights fixtures that don't do well in the cold. Find one that says it is good in cold temps and hold them to their word. They're out there!

Not really. Some older fluorescent shop lights struggle in lower temperatures until they warm up. I have these and some older versions. These come on and warm up fast even down to 30 degrees.

I don't think that the fixture itself needs to be at a certain temperature, but the bulbs do. When my shop is cold the bulbs are dimmer than normal when first turned on, but they warm up quickly until they are fully illuminated. By cold I am talking around 45 degrees or lower.