We need just a little more detail. Where is this room going to be located ? Main level house, basement, garage ? All of which would require slightly different needs in environment control.
The ambient temperature of the grow room (temp of room surrounding the actual grow room/tent) will affect the ultimate temp of the grow room itself.
That being said, there is a way to control the ambient Temps as well. if you can pull the hot air from the light/hood and grow room, and send that air to another portion of the house, you should effectively be removing most/all heat being produced. Which of course would result in little to no temp increase.
On the other hand if your just pulling air from the tent and exhausting it into the ambient enviroment, your basically just prolonging the issue.
But to answer the question directly, yes that fan will work, if you exhaust correctly.
For the filter and smell, that's highly strain dependent.. But golden rule, better to be safe than sorry.
If your still debating plant numbers I can give you advice. Although it will always be trial and error when it comes to canopy management. ALWAYS. No matter how much you read, experience is always wins.
Anyways, the most ideal way would be to do 1 plant per square foot. Only veg for maybe 2 -3 weeks tops depending on strain. No topping, but maybe some lollipop (trim lower branches) to reduce popcorn nugs. I like this 1 plant per square foot because regardless of the room size, you always know the veg time, and the training for each plant is minimized. This results in less chance of untamed bushes producing ounces upon ounces of larf. If 25 plants is too many I would suggest 9 plants veg'd for 4 weeks. Topped once early in growth and lollipopped.
Whatever you choose, just remember to take note of the veg time, snap a picture with the plants before they get put into flower so next round you have a good idea of what your babies grew into so you know to to train/prune accordingly.