Since your belts haven’t been changed since the Civic rolled off the line in 1972, maybe it’s just time…
Seriously. What year is this Civic? How many miles are on it? Why wouldn’t you change the belts? Saying your car is making a noise and “never had the belts changed” is like saying I smell something bad and never change my socks. If you are trying to save money by not changing belts, forget it. Changing a belt is like changing a filter. It’s just a normal thing that has to be done according to a schedule or you are asking for trouble.
I will add that your car has a timing belt. A timing belt will not give you any warning of a problem. It will just break and your car will immediately become a very large paperweight. Timing belts are changed on a time/mileage schedule. They are not optional.
So do yourself a favor and take out your owner’s manual (or find one online if you don’t have one) and get your car up to date on maintenance.
Saying “hot a/c” is completely ambiguous. I am going to assume you mean that the noise goes away shortly after you turn off your interior blower fan and/or HVAC regardless of the temperature setting. That interior blower fan fan will blow hot air or cold air depending on where you have the temp setting. The blower fan can make noise for several reasons. The fact that this is an at-idle noise only is more suggestive of a belt or pulley issue. But it doesn’t rule our a noisy or otherwise compromised blower fan.