Water cooling lights

So Im entering new territory here.
Thinking about putting an ice box on my lights.
Not sure about pump sizes and chiller requirements.

Setup:

2 X 1000w HPS aircool magnum XXXL reflectors running in series to a 6CanFanHO.
My issue is that the air leaving the grow room just gets dumped into the larger surrounding area and I have no way to vent it out.

So Im thinking of adding a single ice box at the second hood output or maybe even one on each, not sure yet.

Now..... will the chiller end up creating more heat then the system can remove? if so the whole thing kinda becomes pointless cause I cant get heat out of the space as it is. What size chiller would be needed for a single and double setup and about what sized pump?

Also thinking of maybe putting one on the output of the ac unit I run as well, same issue just dumps heat into the larger outer space with no way of getting that heat out of the room. Maybe a combo of three - one on each light + one on the ac output?

Toying with chillers is new to me.

i dont understand why there is no way to exaust the room. are the walls concrete or something that cannot have a hole put in them? maybe try venting out thru the floor which is what i do and it works fine. your probly right about the chillers putting off more heat that you can control and most likely your gonna spend a bunch of money for nothing. if i were you i would figure out a way to vent the hot air out thru a window a.c unit or something. good luck brother