On top of that, as we experience higher temperatures, many people also crank up their air conditioners—which emit more heat-trapping greenhouse gases into the atmosphere.

This is not correct. Air conditioning units do not 'emit more [...] greenhouse gases'. Air conditioners use a refrigerant--usually R134a--which does have a high global warming potential (GWP) compared to methane or CO2, but that refrigerant is in a closed loop; it's not going anywhere unless the system is damaged. Most a/c failures aren't from refrigerant leaking out of the system, and the system no longer being able to effectively transfer heat, but from the compressor motor failing. When the compressor fails, in most cases you can evacuate the refrigerant, replace the broken part, and then recharge the system. (The fact that they can be repaired doesn't mean that they usually are repaired. Which is shitty.)

What is true is that a/c units emit heat themselves. An air conditioner moves heat from inside a space to outside of that space; in the process of doing so, the a/c unit itself is creating an additional small amount of heat from the function of the compressor motor, electronics, etc.

Beyond that, most electricity that's used to run a/c systems--and every other electrical device--is produced from burning fossil fuels. So if there's more demand for electricity--such as from a heat dome that has everyone running their a/c full-time--then yes, more CO2 is going to get pumped out into the atmosphere. But if your electricity is coming from sources that are largely emissions-free, like solar, wind, or hydro, then air conditioning is a negligible source of heat.

tl;dr - don't feel bad about using your a/c when heat rises to dangerous levels; agitate at a local, state, and national level for renewable, carbon-neutral ways of generating electricity, and for more efficient use of electricity.