which islands to beat the heat?

It will be very hot in Crete. The Ionians are higher up, but it's still gonna be hot there. Choose a hotel room that is not west facing.

No one knows ( not even meteorologists) what the weather will be like two months in advance. You can have a look at the history of temperature, humidity and rainfall averages at www.timeanddate.com by scrolling down to “weather” entering the location you’re interested in and then selecting “climate” on the right side. Humidity can be as important as temperature.

Crete and Rhodes are the two most southerly large Greek Islands, so they are the hottest. A heat wave lasts for less than a week. No one can predict when the next one will happen.
Ferries between Rhodes and the Cyclades Island group is problematic. Flying requires connecting through Athens.

Don't plan your vacation based on weather forecasts and data from previous years, especially nowadays given climate change.

Last July almost 20,000 tourists were evacuated from Rhodes because of wild fires, more than 15% of the island burned. This year the drought is already affecting most of the islands and particularly the Cyclades Islands, the temperature in Crete reached 44.5°C (111 F) last week.

If you don't like the heat I would say to avoid Greece in particular from mid June to mid September, or maybe go further north to the Sporades Islands or the North Aegean Sea islands (we will be in Lemnos in September).

Regarding transport, from Rhodes there are no direct flights to the Cyclades Islands and no ferry to Paros or Amorgos.
The only possibility of reaching the Cyclades by ferry is 3 times a week to the island of Syros (night ferry, 11 hours journey).
There are no direct flights or ferries from Rhodes to the Sporades or North Aegean Islands.

There is a daily flight from Rhodes to Heraklion with Sky Express.

The entire island of Delos is an archaeological site with restricted access which can only be visited via organized tours from Mykonos or possibly Naxos or Paros.

Thanks for the tips about travel from Rhodes to the Cyclades! That switches things up... Now I'm back to wondering, which 3-4 islands should we visit? How do people decide? For our last trip, we just followed Rick Steves' Peloponnese tour and it was awesome, but I don't see the same kind of trip guidance on this website for the islands.

We're coming from the US (west coast) and hoping to avoid traveling through Athens. We'd love to have our European layover city be somewhere cool so we can add a day to explore.

Do we stopover in Venice and then fly to Corfu (only $25 flight!) and explore the Ionians? Stick with Rhodes and just explore a few Dodecanese islands nearby? Or fly into Mykonos or Santorini (really want to avoid the super touristy places though) and still be able to do Amorgos and Delos and some of the Cyclades?

Seriously, how do you decide which islands to visit? I'm feeling so stuck!

Lufthansa has flights to Crete (I think Chania and Heraklion), so you could possibly breakup the trip in Munich.
You already took my usual suggestion--the Peloponnese. I just don't have the patience to deal with island travel. My next visit will be to the north, unless I make it to Crete first.

I didn't think about picking one large island and exploring it! That's not a bad idea, we'd save time traveling from one island to another. Would you recommend renting a car if we just went to Crete? Although, another person said Crete tends to be very hot...

I don't think you'll be beating the heat on any Greek island in late August/early September. Best to just do as the locals do--enjoy morning and evening, take it easy during the day!
That said, I'd love two weeks on Crete.

Crete is huge and you'll definitely need a rental car and at least a week just to barely scratch the surface of what there is to see and do there.

Many European cities have direct flights to popular tourist destinations in Greece other than Athens.
These are mainly budget European airlines: RyanAir, EasyJet, Volotea & Transavia.

So you can find direct flights from a European city to some islands such as Corfu, Crete (Heraklion or Chania), Rhodes, Kos, Skiathos, and of course Santorini and Mykonos.

With these airlines always check baggage policies carefully. For example, the Venice-Corfu flight at €25 with EasyJet will cost you €83 with cabin baggage and €92 with checked baggage.

You could easily stay more than a week in Crete. Note that from Crete you can go to some Cyclades islands by ferry:

In September Seajets operates the route: Heraklion→Santorini→Naxos→Mykonos→Paros→Ios (every day)

Fast Ferries operates the Heraklion→Santorini→Ios→Paros→Mykonos→Syros→Piraeus route (3 times a week)

Departures are early in the morning.

You can also fly direct from some European cities to the island of Lesvos in the North Aegean. It’s the third largest Greek island and offers a variety of scenery and beaches.

We once spent 3 weeks there, in 4 different bases: Vatera — with a long sandy beach; Skala Erresou, a gorgeous beach — with daytrip opportunities nearby; Molivos, topped with a Byzantine fortress; and Mytilene the capital, which you’ll fly in and out of. We actually stayed outside of Mytilene at a wonderful resort called Votsala, with amazing breakfasts served under the olive trees in the courtyard, a private (rocky) beach and free beach toys (kayaks, etc.) and one of the most hospitable staffs you’ll ever find.

Lesvos is off the beaten tourist track, so prices are lower. People are welcoming & the food is delicious.

We just returned from Crete. Wonderful time. Definitely rent a car. A large island with things spread apart. We stayed 4 nights and just touched the surface. Next time we will stay longer.

We spent two weeks on Crete, stayed in Chania.
Can you change your dates? It was beautiful, not hot, when we visited Crete in late Sept, early October.