First loose the heat lamp.

Second loose the foil that will create heat spots, Mylar is what you want or just use flat white paint.

Third pick up a few 40w CFL they are cheep. There are a few great threads on the exact model to buy.

How are you going to deal with exhaust and fresh air in if you put the cover on?

Cleaver idea too btw on using a tub that way!!

You don't have a lot of room to grow from seed you need to keep it small so pray for a female on your first try. If you can get a clone it would work the best.

What are you going to do about odor control?

It will smell up your cloths that hang in the closet.

Don't think you can hide this from people in the same house they will know at some point.