If you cannot manage a full-time brooder, yes that would probably help. You may or may not need a lamp for the outdoor times, depending on what temperature it is that day and how long you keep the chick outside. Even newly-hatched chicks with a broody hen will run out to see the world, then snuggle back under her to warm up, then come out again (over and over all day long.) As they get older, they spend longer times running around, even in the cold.
(Posting again, because I forgot to directly answer this in my previous one.)
