Very little or you will send the birds into shock if something goes wrong and they will refuse to go out ever. Just enough to keep the temps above 0-10F.
Sweeter heaters or other safe radiant heat sources. Don't use heat lamps, they burn down coops, break easy, etc.
Only heat if your winter temperatures regularly hit below 0 for more than a few days each winter or you have very delicate breeds. We do not need heated coops where I live and we tend to get about a week at 0 thru -10F each winter. The rest of the time it's usually around 10-25F. The worst we've seen from this is some dehydration and the tippy tips of frostbite on bigger single combs.