You didn't say if there are any other birds using the house or not, so I will assume not. Nor did you say how big it is.... but it does sound like your coop has a bottom.
I will make the following suggestions based on what I understand of your set up -
1. Get bales of hay and fill in that area under the coop, and maybe even stack around it on 2 or 3 sides. Cover the bales with a tarp to help them last until your ready to
compost 'em in the spring. There's your insulation. Close the vents and windows, except for on warm days.
2. Now put deep litter inside, leaves would be best as they won't off gas like cedar chips, which is not good for birds. Deep litter is nice for the birds to scratch in and keep their droppings covered and themselves entertained.
3. Install a light close to the floor, about 10" - 12" up and in a corner. The birds will come closer or move away to regulate their need for heat. Put the light on a timer so it comes on when things cool off and stays on until the area warms up again the next day. Check the light, timer and wiring often to make sure all operates safely as you intend it to.
4. Have inside water for them that won't freeze.
Harden the chicks off a little in their current location, and then when the weather is cooperating for a couple of days move them to the coop. They will be fine. You may need to raise the light in a few months when they have grown.