They are probally not hardy in your zone.
Keep them as a house plant. More than likely they will go dormant but will return next summer. I plant mine in the same pot as one of my upright elephant ears so I can keep track of it. It always goes dormant and is very very slow to re-emerge. Mine are just now starting to look good and it's time to bring them in. They will last a few more months. I keep them pretty cool during the winter and do not water often. With enough warmth they may last all winter and never stop growing. I have seen them for sale as house plants all year long. I just have never tried it.

I have a couple in the back yard..but they seem to suffer even in our somewhat warmer zone. In the ground, they are veeery late to emerge. The majority of these, I have in assorted pots on the back porch. I just store the pots in the garage, after the foliage wants to die back down. I keep the pots completely dry...mainly 'cause I never remember to water them. Mid-spring I set the pots back out. Peacock ginger, for me, is slow to re-emerge in the pots even. Don't throw out your pots next spring, because you think they are dead....be patient.. they love warm nights.

All of ours are in the ground here and they all start re-emerging in late March/early April.
The Kaempheria are naturally deciduous I believe (if I am wrong I am sure someone will correct me) and while they will "stay up" as houseplants they really like to go on and go dormant for a rest.