outside air to cold for growroom?

I am growing in my half basement, L12'xW12'xH6'. I have no other source of heat down there then my light 1000w hps with air cooled hood. I wanted to run a sealed system for cooling my light and use it to heat my living area up stairs. I have a 200cmf fan hooked to a humidistat which exhaust the room, and a passive 4" intake. My concern is now that it is getting much colder outside (nights are in the 20's now thats when I run my light.) is the passive intake going to make the room to cold. I really want to take advantage of the higher C02 levels in the air now that it is winter. I also want to mention I am not taking air from outside to cool the light,I have a cold air return vent hooked to the intake side and after it exits the hood it is vented in to my living room.I figure I could kill 2 birds with 1 stone,get the most bang for my buck,if the light can serve 2 purposes. Oh yea , I only use a 4x4 area for growing,its not enclosed its just a wood frame enclosed in Mylar. Any ideas greatly appreciated.

you have a filter on the intake? the 1000 watter will be putting out some heat in that 4x4 area... Think about sealing the hood? meaning

COLD AIR INTAKE from outside >ducting>hood>fan>ducting out grow room? then you could just get a 4'' booster fan for like 15 bucks and put it on the timer to refresh the room with cold co2 air? IMO 20's are way to cold to introduce straight into to growroom, especially at 200cfm, but my air cooled lights love it

Thanks for the advice ,but I think u misunderstood. I have a passive intake,and a 200cfm exhausting the room. I am a little hesitant to pull that cold air into my light, I do have a sealed light hood but I wanted to use the exhaust to heat my living space upstairs. The cooling for the light goes like this. cold air intake from upstairs temps in the 70s=to duct work about 3feet of 8"=400cfm fan=to light = to duct work four feet of 8"=to vent in living room floor to heat the room.
What I was wondering I guess is would my 1000 even though its being air cooled,still produce enough heat,to heat my grow area?