Temperatures can be deceiving. It may be nice outside but a house or car can create retain heat from the sun even if temps outside are cool, reasonable, and breezy. Right now, it's about 75, slightly windy, and cool outside with low humidity. But inside, it's over 80, hot, and stuffy. Even with an open window (while I'm home) it's not enough to keep the inside of the house and the cats cool. With windows closed, it would be unbearable for the cats.
When we are gone, we pull shades, run fans in locations that stir the air and place them where they won't create a hazard for the cats (you don't want paws playing with blades; and you want to make sure no other items can get near the fan to create a hazard, or an electrical short, or fire hazard.) There is one window where we can run a portable AC unit and not be worried about someone breaking in (and there are various means one can use to stop a window from being opened any further.) (Portables that exhaust moisture out through a hose [as opposed to dripping water out through a hose or into a bucket] are nice because a screen doesn't need to be removed from the window for the exhaust system to work.)
When we are home, we pull shades, open certain windows, run fans, and run portable AC units (see previous post.) When Myrna was still with us, I only opened windows when a cool but not cold or hot and humid breeze came through because too cold and too humid air created congestion issues for her. I used a portable table thermometer to track temp and humidity. I could set it in the window to see what was the actual temp as she sat in the window (the temp was always different from actual outside and room temp.) Sun and shade in a window or room will create different temp situations and humidity levels that may make it difficult for your HCM or any cat or pet to breathe. Monitoring indoor temps with the portable thermometer allowed us to quickly make adjustments for Myrna's health.
Here's a suggestion for a portable room thermometer, similar to what we use:
https://www.amazon.com/Easy-Read-Thermometer-Fahrenheit-Temperature/dp/B012TIU1IG/ref=sr_1_1?ie=UTF8&qid=1464799936&sr=8-1&keywords=portable+room+thermometer
