You can try it, but please don't put plants in there. You have 90 cubic feet, I have 125 with a 600w HPS and it's enough to raise the temperature by 18 degrees c (32f) without my extractor fan running, and there's a 45w oscillating fan moving the air around.
Even if you raise the light, the room will still heat up if you're not getting rid of that heat somehow. A swamp cooler or ac would lower temps a bit but it's far easier and more efficient to move air rather than cool it.
That's ignoring the fact that if the plants fill the room, they'll soon deplete the co2 in there until growth stops. You could run co2 enrichment, which would allow your plants to tolerate higher temps, but co2 controllers aren't cheap.
Can't you extract out of the door? You could get some panda poly, have the door open say a foot, then staple the poly to the doorframe and fix some velcro to the other side so it laps over the side of the door, then make a hole in the bottom for an intake duct (with a light trap if necessary) and another at the top with a fan pulling air out, preferably ducted out of a window or somewhere.
I know it's a bit out there, and not very stealthy, but I have your plants best interests at heart.