Air-cooled lamp. Do I need more fans?

This will be my first grow. Ever. For now I have a larger fan for exhaust, a smaller for intake, and was planning on having ducting go straight from intake at wall, through vent to lamp, out exhaust and out of room. Then I realized that (especially if my reflector has the glass seal)... Don't I need OTHER air getting pumped in/out if room? I can't afford another fan until I make something off a grow to put back into my system. What do you guys think? One possibility I've entertained is having intake push air into room, then having my exhaust fan pull air straight from the room through the hood and out if that makes sense.

ANY AND ALL INSIGHT APPRECIATED.

That's a closed system for your light, that of course is ideal for heat but as you point out that type of setup requires 3 fans.
A) Intake > smaller fan > light > exhaust out room.
B) Intake #2 > Larger fan > into room.
C) New fan hanging in the room > exhausting heat / odor air out. Preferably hooked up to a filter of some sort.

If you want only 2 fans.
A) No intake, just large fan hanging in room > light > duct exhausting out room. Optionally a filter at the open end of the light before the fan.
B) Intake w/ fresh air > smaller fan blowing into the room.

You shouldnt need an intake fan, you can run

intake >ducting > hood > ducting >exhaust fan > out

If you run a dedicated intake for the hood, another exhaust fan will draw air in to the room. You wont need an intake fan here either.

A lot of people with smaller grows dont run dedicated intake for their hoods. Just the air moving over the bulb cools the room. Whilt its not going to cool as well as a dedicated intake, it will help with the heat from the lamp.

I run

Filter > duct > hood > duct > exhust fan > out

I have passive intakes to provide air exchange. The passive intakes should be at least 2x's the size of the exhaust and located opposite the exhaust and towards the floor.,