building an extractor fan soundproof box?

I have a 400cfm extractor fan- an eco-plus supreme- I have a duct muffler attached- no noise outside of growroom but the fan is rather loud inside the room- fan is supported with bungees- if I build a box out of acoustical tiles and house the fan will this be a problem for fan? It is sealed so I assume housing it would not be too much of a problem- I am worried about containing that motor heat and would that cause any problems- after 3 months of building room about ready to fire it up

I don't think that would be a problem, there are no air vents on the outside of the fan....

I have something similar, my fan is hanging from the ceiling on bunji cords inside a box made of plywood which is heavily insulated. It's been up there for several years without problems.

keylime