Carrots need to be sown where they will be grown, so unless you plan to actually grown them in the ground inside your greenhouse not a good idea.

In fact not really a good idea anyway as they will do far better outside. The need a fine, sandy tilth with no compost.

I suppose you could, as I intend to this year, grow carrots in big pots, then you could haul them to wherever seems best. (we have very shallow, stony soil in a lot of our vegetable garden, which has given us mediocre crops in the past, and I'm hoping to not only give them a nice deep run of sandy soil, but plant them in succession, too) I really doubt that even starting these off in a greenhouse, heated or not, would give them much of an advantage.