If your computer is shutting down and refusing to restart at an ambient temperature of only 88F, then you definitely have issues beyond just your home air conditioner not working.

Do you have any software installed to read the temperature sensors on your motherboard and chips? The appropriate software on Linux is "lmsensors", but I don't know about on Windows computers.

Definitely clean your fans, make sure they are all spinning appropriately, check routing of cables inside your box to make sure they are not blocking airflow, etc. It could also be that your thermal paste between the CPU and heatsink has aged (rare) or was never correctly applied in the first place.

At no significant load, my CPU temps typically run 25C (77F), which is about 6F degrees above ambient in my house. When the computer is under significant load - transcoding video for example - CPU temps rise to about 31C or 32C, about 18F degrees above ambient. This same computer had an older CPU a few months ago (I upgraded the box recently). That older CPU had developed heat shutdown issues. Turns out the thermal paste had degraded over the years. That old CPU would send the box into thermal shutdown when transcoding video because cooling was far from adequate given the thermal paste issue. When diagnosing the problem, I watched the CPU temp sensors in real time. The box would shutdown at a little over 100C. That is quite high for a CPU! Well above design limits. But 100C is 212F, and you most certainly should not be hitting those kind of CPU temps at your house ambient of a mere 88F, no matter how heavily loaded the box is. After just a few thermal shutdowns, you should probably consider your CPU might be on it's last legs from heat stress, and consider replacing it.

Back in the old days computers were more heat sensitive. I remember huge computers huddled together in special highly cooled rooms. We'd have to wear light jackets to keep warm when working in there. But home PCs are not anywhere like those beasts from the old days.