Heat pump simply means unit cools and heats with same compressor. If I understand your problem is not being able to raise windows for fear of intruders. A central air,window unit(s) or mini-split would be my first choice but here's one way of ventilating house day and night without fear of intruders. Buy a used blower out of a gas furnace from a HVAC dealer. They either give the old units to scarp men or sell them for about $5 at scarp yard. You need one from a gas unit so it is 120 volts. Cut a hole high as possible through an exterior wall and mount blower to exhust air through the hole. There are simple louvers to screw over hole outside. The blower is 3 speed and easy to wire and control with a 3 speed switch. CLICK HERE to see latches that allow raising ALUMINUM windows enough for air to enter but not enough for a person to fit through. If you have old fashion wood windows you'll have to improvise with a nail,screw or stick. Blower will help when mounted in a window but is 50% more effective if mounted near ceiling. To get best result without cutting hole through wall,do the following. From a HVAC supply store,buy 2 duct take offs of right size to fit on each side of blower. CLICK HERE to see an example picture but you can buy them everywhere. Also buy 1 duct which will be cut in half. If they will sell only 2 zip ties get those but you can also use duct tape to secure duct to take off. With blower mounted in a raised window and window secured to prevent being raised farther ,attach duct on take offs then secure open ends on or near ceiling. A much neater way is exhusting through ceiling but that requires more skill and tools. Don't let the dealer soak you for more than $5 because that's more than they get for them. CLICK HERE to see an example of blower.

I'm reluctant to get AC because of the climate implications, but I wish there were a way to disperse the heat inside. Is a heat pump a good solution?

I live in the Seattle Washington area, and these heat waves are new to us!

You mention this problem without telling us your current heating system. We know you don't have AC, but this doesn't lend enough info to really direct you.

A heat pump is the same as an AC except that it has additional controls to provide heat in the winter time. A heat pump costs more than AC.

Depending on your current source of heat (winter time - not summer heat wave) --- if you are on say electric heat, then a heat pump wouldn't be a bad choice for your climate. Your climate isn't one that is considered cold climate or hot climate more of a mid range rainy type climate.

If your current heat system is something other than forced air type (air to air transfer via duct work) that can add additional costs.

If your heating system is natural gas forced air a heat pump could serve as a back up to that system but at additional cost. You can argue these kinds of things a myriad of ways.

Natural Gas type heat is extremely hard to beat when you factor in everything.

Adding in ventilation in a more humid climate won't be that comfortable in my opinion. Then the fact that you're then living in a wind tunnel. I wouldn't consider that comfortable either even if humidity wasn't an issue.

I service the Katy, Texas area.

"Natural Gas type heat is extremely hard to beat when you factor in everything."

The OP didn't ask about heating, Ray, but since you opened up that discussion, consider that Seattle electric rates are lower than the U.S. average and pretty stable (there's a lot of hydroelectric power generated in the Pacific Northwest.) By contrast, natural gas cost $1.26 per therm in June 2022 compared with $1.18 in June 2021 (and it's less expensive in the summer than winter.) When you factor in the effects on natural gas prices due to Russia's declining supply of natural gas to Europe and the (unrelated) potential for carbon taxes in the U.S., I'd think twice before recommending a gas appliance to someone in Seattle, WA

What works best in Katy, TX isn't necessarily what works best somewhere else. Some simply analysis on your part will help folks avoid bad choices or at least make more informed ones.

It's a 1955 Rambler, Charles. It wasn't built yesterday.

Natural Gas has been used as a heating gas for how long now?

They use Natural Gas nation wide. Not just in Katy, Texas.

Ray,

Natural gas has been used as fuel for some time. So has wood. So has coal. So has uranium. The most economical choice for heating will vary from one locale to another depending on a number of factors.

We don't know whether the OP has access to natural gas. What we do know is that electric rates in Seattle are below the national average and stable.

Blanket recommendations are rarely appropriate. If you've concluded that natural gas is tough to beat in Seattle, please share with us some calculations to back up your claim.

"Friends just open their windows at night to let the cool air in, but I live alone and don't feel secure with the house open at night"

Be brave. Open the windows. Cost: $0.

"Be brave. Open the windows. Cost: $0."

If you are concerned about security, you could get decorative window bars installed.

You could install a device which does not allow the window to open beyond at specifed amount. This would let air in but not an intruder.