I would get him footed PJs. You can get them in both thin-cotton versions (I love Children's Place's ones) and thick blanket versions (they have these at Costco right now at a GREAT price!). Also, maybe he would be happy in a sleep-sack. They do make bigger ones now for toddlers and older kids. They have foot holes for walking, but they can pull their feet in to sleep:
http://www.inventiveparent.com/cgi-bin/shopper.cgi?preadd...
To answer your questions, no, it's not harmful and he won't get sick from getting cold. Maybe he just gets really hot when he sleeps and needs his feet out (I know I do).
As for a space heater, I would really recommend against it. I thought about one for our little girl's room (her room is freezing when it's cold out and it seems to get the least heat in the house). Well, I found out that according to the National Fire Protection Association, space heaters are a leading cause of home fires during the winter months. And that according to Consumer Product Safety Commission, there are more than 25,000 residential fires and 300 deaths caused by space heaters each year. I found this research online, so if you want to look into it more, please do. :-)