It makes sense as to why your temps are high. You are pulling warm, ambient air into the hood and pushing it into the attic. There should be one fan for the hood and one fan for the filter. You could hook only your filter up your current setup and it would be ok. Because we use sealed hoods, the air we use for them doesn't need to be filtered. It can be exhausted anywhere (provided the sealing gaskets are working properly). You should be drawing in cool air from outside your house for the hood and exhausting it outside the house as well. Again, the air from your sealed hood doesn't smell and does not need to be scrubbed. Each of my tents has an intake from outside for the hood and then one just so it has fresh air entering the tent. I do combine the exhaust ducts into one for the exit, but that happens after the tents and doesn't have anything to do with the temps inside them (or the area the tents are in).
Also, try not to give it too much venting. You do want to create negative pressure in the tent to contain the smell.