Try shutting all the ac/heat vents to the rest of the house and fully opening the one in your room. The other vents will still leak plenty. I used to live in an old farmhouse and that's what we had to do. Every spring and fall we swapped the vent openings and closings to regulate the individual rooms because of the poor heat/ac distribution. It was so stupidly setup. The smallest room had 2 vents while the biggest rooms had 1 vent and the medium size living room where the thermostat was had 2 vents and was right in front of the door to the basement that always stayed 68F year round. It was a nightmare trying to keep every room comfortable.
What's the longest you will be gone during the day? You can freeze containers of water and set them in front of a fan that blows near but not directly on the chins. Over the cage would work best because cold sinks and heat rises. You can gain up to 5F that way especially if you are in a dryer area but the frozen bottle(s) need swapped every few hours and it takes up freezer space. Regular air movement does nothing for chins because of their thick coats and lack of sweating so just a fan by itself will do nothing. If you have a metal floor pan putting a frozen container in the cage will chill the whole floor pan along with metal or ceramic tiles many put in the cage for chins to lay on. That's how we got through the end of last fall when our ac went out and the temps were dropping the next week so we just had to get them through a week of 78-80F in a house that heats up fast with 4 computers, every modern game system, a heated room for desert hedgehogs.... The problem is eventually chins will grow curious and chew through plastic containers in their cage. Fabric sleeves might have to be made or roll them under a fleece liner. It's not a great solution but it can buy you some time on hot days.
The cheapest, easiest, safest, long term solution would be to buy a window unit for your bedroom but that may or may not be your call. The standalone units that just have a tube going to the window for drainage are more temporary but much more expensive for much less effect.
