How cold does your area get in the winter?
If the rooster is a full-sized adult, without frizzle or silkie feathers, he will probably be warm enough just roosting in a spot with no wind at night, and being able to sit out of the wind in the daytime. So you might not need the heat.
For space, he definitely needs enough space for a feeder and waterer, and enough room to stretch his wings out. He should have room to dustbathe and scratch around a bit in his run.
The usual space quidelines seem awfully cramped when you scale them down fo one chicken. In addition to the space filled by the feeder and waterer, the minimum space required for one chicken is often considered to be:
4 square feet in the coop
10 square feet in the run
1 square foot of ventilation in the coop
1 linear foot of roost
One way to meet those guidelines for a single chicken:
Have an area 8 feet long and 2 feet wide, with the 2 or 3 feet at one end being the coop. Put a roost bar across the middle of the coop area, about 2 feet up. Roof the whole thing, and put solid back & sides on the coop part. Leave one side of the coop open, facing the run, to provide lots of ventilation.
If one long side is against the hens' run, he will have plenty of contact with them. Consider a windbreak on part of the other long side, depending on which way your wind usually blows.
The food & water could be in either the run or the coop portion, depending on weather and temperature (but don't put them under the roost!)