Please, PLEASE don't use a space heater. Chicken coops, chickens, all the dander and dust they create, and heaters just don't mix.
I have used a heater, an oil-filled electric one, in an outbuilding to provide supplemental heat for chicks, but it was on the bare floor, not in the brooder with the chicks and the building was wired for electricity.
Here's a pic of that set-up. You can just see the heater in the bottom right hand corner:
The chicks can go out to a draft free, predator proof coop with a heat lamp as a safer alternative. Just be sure and doubly secure your heat lamp. For example, I use both a chain and zip ties to secure the heat lamp. THE CLAMPS THAT COME WITH THE LAMPS ARE USELESS AND SHOULD NOT BE RELIED UPON TO SECURE THEM. Also, make sure the lamp has a ceramic socket, not plastic and that you don't use a higher wattage bulb than you need.
You don't need to heat the whole coop. Just section the chicks off in a smaller area and hang the heat lamp in that area. They will go under it when they feel the need to warm up; just as a broody raised chick goes under mama whenever they feel the need for a warm up. They don't stay under mama full-time.
Good luck with your chicks