Mate, I hope you won't but I think you are going to have issues with the way you are trying to do this
First off, I have a 3x3x7 sealed space in the garage @ about 76 degrees ambient. My space is insulated too about R6, but keep in mind it is wood construction, not a tent.
I have a designated widow type ac for this space and it comes on every 4 min. about in order to maintain my temps at about 81 degrees, it runs like 4 min. off 1 min on. Keep in mind AC also deals with dehumidification if done right! My light is completely isolated from my grow cab (I use co2 in a sealed enviro)
Your AC will not be sufficient I think the way it is run at this point. It lacks the necessary control you need. I would assume that your t-stat is somewhere in your house close to the air intake, which in turn means that your t-stat is rendered useless for your grow area, since it does not know what the temps are in your grow space. At best you will be wasting tremendous amounts of energy since you have to set the t-stat at an very low arbitrary temperature in order to make sure that you are not going out of range. This would mean that your house temps get waaaaay to low, and your ac unit will most likely ice up due to not cyceling off enough. There are ways , but by far the cheapest, best way would be to get a little indevidual window unit (check my grow cab/https://www.rollitup.org/grow-room-design-setup/86604-grow-space-build-sealed-no.html , maybe like 5000 or 6000 btu.
I think you may be able to make your set-up work somewhat, but your parameters will suck, you will not be able to use co2 due to the perpetual exhausting you are doing. I disagree with Bonz, Co2 injection is rather scientific and certain parameters need to be maintained in order for co2 to make a difference.
A good scinario would be:
Lights on:
Temp:81-83 (w. co2 only! IT NEEDS THE HIGHER TEMPS IN ORDER FOR THE STOMATA'S TO OPEN MORE AND UTILIZE THE CO2)
Humidity 50-60%
Co2 1100-1500 maintained with a controller (below 800ppm co2 will not make a difference, above 1500 will not give much added benefit. The shit is expensive so why waste it!
I do not exhaust during lights on, but I do run a intake in conjunction with and exhaust system that comes on during lights off. (Back-draft dampers are needed here so you do not loose your co2 during lights on.
Hope this helps somewhat, I'm sure I have left things out, but I'm happy to help out if I can!
Unity