yea heat is going to be an issue, once u start to flowering the plants are going to get 3/4th bigger by the time its over,You need a High Pressure Sodium light and the ballast to go along with it, no way thats gonna fit and be far enough away for heat issues, even with the other lights it will be too close and too hot. a bucket would be the only size container that would fit, and that takes up like a foot and a half. i have attached some pics of my Deep Water Culture System and my grow, look at the size, no way u can fit that in a 3 foot Dresser.

You need a larger space, it will only be ok for a very short mount of time, like 2 weeks at the most, and then the plant will be big. you still havent answerd how you are going to get ventalation to your plants in the death trap? u cant fit a fan in there.