How hot is it in the closet? That is certainly not where an A/C should
be placed to dump heat. If it's very hot in the closet, that will
limit how effective the unit can be. I'd measure the temp of the air
coming out when you first turn the unit on. Wait about 5 mins, then
see how cold the air is coming out. I'll be it's a lot colder. If it
is, then you're problem is the closet. If you can rig a fan in the
closet to move air in/out, that would fix it.