Summer rental

Marbella will probably be cooler than Phoenix. How could it not be? But southern Spain is very hot in the middle of the summer. Timeanddate.com has actual, historical, day-by-day weather data going back about ten years. Here's Marbella in July 2021; I encourage you to check additional years to get a more accurate picture of the range of weather you may experience.

https://www.timeanddate.com/weather/spain/marbella/historic?month=7&year=2021

I'm always a bit concerned when people speak of using a smallish place as a base for an extended period of time. A smallish base nearly always means a traveler without a car is quite limited in the practical side-trips available. Marbella is a significant bus ride (Rome2Rio says about 55 minutes, but I haven't verified that) from Malaga. Or you could take a bus to Fuengirola and pick up the cercania train to Malaga there. However, the cercania from Fuengirola to Malaga would still take at least 45 minutes, so the bus+train combination would be slower than sticking with the bus.

Rome2RIo (not always reliable) says Ronda would take perhaps about twice as long, Granada about 3 hours, Cadiz and Jerez between 3 and 3-1/4 hours and Seville about 3-1/2 hours.

I suppose Marbella could work if you will just want to visit a bunch of other coastal resort towns and Malaga. I would find it way too isolating for more than a few days, but then I am not at all a beach person.

If you want an area that's reliably not-hot about 90% of the time in the summer, look at the northern coast of Spain between Galicia and the Basque Country. Those are great summer destinations.

Marbella is a poor choice if transportation is important for you, and most of it is a rather charmless 1970s-1980s development. Also, while Marbella itself is of course cooler than Arizona, the inland regions easily break the 100°F mark...
This being said, if you are set on Southern Spain and OK with hot temperatures anytime you leave the coast, have a look at Cadiz. It has a lot of charm, great beaches (ocean beaches, beware), and good connections to other places in the region.

But I second the recommendation to go north. There are plenty of pleasant bases that have decent public transport.

If you like a large town/small city, San Sebastián is an excellent option, if popular and rather expensive.
For somewhere more resort-like, Zarautz has a great beach and good connections to other places in the Basque Country.
Further west, Cantabria and Asturias have poorer public transportation, but somewhere along the FEVE narrow-gauge railroad can be viable. Ribadesella and Llanes spring to mind, but I wouldn't want to spend more than a month in such places - they are small towns and excursions will rapidly become time-consuming. Otherwise, if you do not need to be next to the ocean, Oviedo is a very lively small city with good excursion opportunities both to the coast and inland.
Further west still, Galicia is stunningly beautiful and culturally very rich, but can get quite remote. Not sure what the best base without a car could be; Santiago comes to mind but it is inland and gets very crowded.

Great advice here already.

Can you be a bit more specific on what you are interested in during your stay? Do you want mostly beach time, or are you looking for sightseeing?

For a prolonged stay, it might be a good idea to consider your knowledge of Spanish, especially if you are planning to stay in a residential area with mostly locals.

There are also many neighborhoods where British or German snowbirds spend their winter. I can imagine that some of those will be quite happy to rent out their apartment for the summer. Note that they have a reason to go there in winter and not in summer.