You probably know this already, but the caulk does not just dry... it cures. It is a chemical process which requires a certain temperature to complete to minimum specifications. My guess is you are pretty boarder line if you will obtain the minimum strength that the caulk is designed to provide. Although, you did put a tarp over the application which will offer additional warmth to the system and may have kept the caulk closer to the required 50 degrees. (Good thinking!)
You will only know in time if the caulk has properly cured. If not, it will crack and weather easily over this next year. At that point you will know that you will need to reapply during a warmer season the next year. If reapplication is needed I would suggest doing your best to pull out the old caulk before spending the time and money to put in new caulk.
The good news, most cement based products will continue to harden over time, so even if it hasn't cured by now it may just need a little more time to cure before you uncover it and allow traffic. I would continue to test a small area for harness and once it feels hardened allow another day or two for additional curing unless you really need to use the driveway.
Next time, if you need additional insulation, you can also spread hay or grass under the tarp to add additional dead air space. The ground remains warmer than 50 degrees for many weeks (in some places, all year) and would likely keep your concrete surface even warmer by trapping the earth's heat from escaping to the cold night air.