Will a bigger tent give me lower temps?

I have a very small tent, 3x2x4', which has a 300w hps in a cooled hood, being cooled by a 6" muffin fan pulling air through the hood and 6' of ducting and blowing it out the window. My temps are at a steady 89 with the lights on, but I would like to get that down below 85. However I dont want to buy a larger fan for noise concerns. Would a larger tent, say 3x3x4, reduce my temps at all? I cant go taller due to height restrictions. Or what about a smaller second fan which blows air through the hood to help out the first fan?

I like the booster fan idea, you can buy cheap booster fans at HD for $20 - 30. Keeping the ducting as straight as possible really helps.

Unfortunately to keep the ducting hidden it makes a few twists and turns. I guess I'll try a booster fan

What cfm is your exhaust fan? Sounds like its not strong enough. Especially since its going through 6' of kinked duct.

Get a larger fan with a muffler and speed controller.

Its just 200-250cfm, I know a larger one would be better, I just don't want to shell out $200 to find that it is too loud