At my old place where I had the closed cabinet, I didn't have AC, so the water temp was around 86F, and the fan brought it down to 78 or even lower if I kept it going.
My current apartment does have AC, but I find that if I close the windows, with all the heat my computer (1000W power supply), my electronics and lighting, nevermind the eleven T5 bulbs running over my tanks, my room temp is 78 to 80F.
I rely on fans.
BTW with the chiller, (if I had one) it will raise the over all room temperature, so even though the water is cooler, the room will be warmer. Just like your kitchen with fridge, as it is adding (whatever horsepower) of heat. You'll need to treat it like an air conditioner and have it vent out somewhere, or somehow keep it in another room, or better yet outside your window under the shade.
Personally I find chillers about as useful as one of those room air conditioners which only have 1 vent hose. Cold air does blow out, but the design flaw of it is that heat is radiating off the hose, so overall there is a zero sum gain in coldness, but a large gain in heat.