Sounds as if he might be overweight. When you say greedy, does he take more than the recommended amount of milk for his age and breed? He should be eating grass as well as milk now, with the milk gradually reducing, then stopping at 3 months or so. Severe obesity in bottle fed lambs can be a cause of sudden death.
On the other hand, sheep pant when it's very hot and seek out shade, so his behaviour is not unnatural if he is a normal weight. Wool insulates against both heat and cold, so I would leave his fleece until next shearing season - he will need it in the winter if he's outdoors, although as Freddiesfarm says you might want to shear him in the autumn if he is to be housed all winter. Do you spin? Lambs fleece is wonderfully soft for spinning or even felting.....