Hey! You absolutely can get one! Glad to see you're weighing up whether or not to get one based on if it is good for the axie
I've got the same situation as you, my tank is in my room. I live in Sydney so it may not get as hot as where you are but I do have ventilation issues.
I have a Hailea 130A and it works great for my 35 gallon. But the chiller does expel a fair amount of hot air, and it is noisy. I turn mine off at night but will run an aquarium fan if it is a hot night to keep the water cool. Does your house have air conditioning? That would help move around the hot air. I don't have air con so I use an oscillating fan near the chiller to disperse the air. You want to keep any doors open while the chiller is running, and maybe the windows too if the air outside isn't too hot. Another thing that will probably happen is there will be a lot of condensation on the outside of the tank. I keep an old "tank" towel either around the tank or under it to catch any dripping water from the condensation. Mine drips a lot on really hot days.
The room will still heat up but so far for me it isn't too uncomfortable, as long as the door is open, fan on and window open. Other things to keep the tank cool is to have either a mesh lid or no lid, leave lights off, no internal filter, a fan on the glass of the tank or over the water.
If you need any help with chillers let me know, I did a fair amount of research before buying one so may be able to help!