Without mentioning a particular temperature, Pelargoniums must not...MUST NOT ever be touched by frost. Frost is a killer of the plant.
Instead, those mid-30's you speak of, are ideal to keep the geranium over winter at.
NO need for water, NO need for light, NO need for heat....the plant goes completely dormant....dries out like last year's prune.....and when wanted to come back as good as it ever was, it is ready, willing and able to do so.

Just cut it back to about 4"...remove all old leaves and buds, inspect the roots for any sign of damage, give it a clean pot to which you place some shards in --not blocking the drainage holes, fresh potting soil, the plant into, give it good light in a western, souther, or eastern exposure....water to drainage...and then no more watering until new leaves form.
At that time, you can begin to fertilize 1/4 rate every 3rd or 4th watering and increase as the plant grows.
Turn the plant every day or so to ensure all parts receive equal sunlight....within 2 - 3 weeks, you will have new leaves coming....and in early to mid May---when you normally put your annuals in, then the pel can go outside during warm sunshine days, back indoors, then out...then in adapting the plant to temperatures as they improve.

Soon, a full flush of flowers will adorn it...as good as it was last season.

Hi Jeannie,
Thanks for the response...but actually, the plants never went dormant in my cool basement...they are now growing really well, and a few are getting ready to blossom. Again,
I'm not concerned about frost, as they will be covered..but I don't want to kill them by putting them in too cold a temperature overnight. I just need to know how much cold they can handle....25 degs? 35 degs? 40 degs?
Thanks,
Linda

If you can keep the temps above freezing (32F), you should be fine. Pellies will actually take light frosts (just below freezing) quite well but I'd avoid exposing them to those temps now after they've spent the winter indoors, are in leaf and some even in bud. Warmer is better but do what you can :-)