sorry, three

Three racks....half wash....and extra dry which I believe is heated dry

Most modern DWs don't have heated dry, including the Bosch. I have the same model shown above, and its drying feature is described here:

https://www.bosch-home.com/us/experience-bosch/tips-and-tricks/frequently_asked_questions_answered

They call it "condensation dry". It works pretty well, but I sometimes still need to prop the door open for a half hour or so before my plastic containers are dry.

salex is correct.....the Bosch extra dry just adds extra heat to the final rise water to enhance drying, so no real heated dry.

Plastic items are about the only things that don't dry in the condensation dry machine.

KA still makes a dishwasher with a heated dry cycle. I would not have a dishwasher that didn't have this.

Yes- KA and the Whirlpool family make a DW with a heated dry cycle. They also have problems with vent discharge damaging adjacent cabinets. This thread is from 2011 but is STILL active. https://www.houzz.com/discussions/kitchenaid-dishwasher-vent-issues-dsvw-vd~2287464

I have absolutely no idea where the vent discharge is on my KA dishwasher, but there is the wood sink unit on one side and a wood panel at the other. I've had both (both were painted) now for 15 years and had ZERO problems with this.

The Bosch 100 Series SHXM4AY55N meets your requirements and is well-rated by Consumer Reports. Drying was rated "Excellent".

I just bought a KA with heated drying. Love this machine. Quiet, cleans perfectly (even dirty dishes unscraped), and nice to look at.

My priority when shopping for a dishwasher was heated drying. I had a Bosch in the past and although it was quiet, I did not like the wet dishes.

It also has a third shelf which I use for all my utensils and tops to plastic containers.

Jane

Most of my plastics get about 90%+ dry in my Bosch without a heated dry, but that does not apply immediately after the cycle finishes. However, since I rarely empty the dishwasher immediately after it finishes (usually not for hours after, to be honest, especially since I mostly run it overnight), it's rarely a problem. The plastics that don't get 90% dry are those that are shaped with a recess, like some plastic lids or the concave bottoms of some containers. For me, the advantage of not having a heated dry outweigh the advantages of having one. YMMV.

Heated drying is overrated. I usually disable it on our KA dishwasher, as I don't want to chance damaging any plastic items. Overall, the KA works OK'ish. But it's a far cry from what our Miele does. With the KA, I regularly have items that didn't clean 100% and need a little bit for elbow grease afterwards.

With the Miele, that never happens. Everything comes out perfectly sparkling clean. And dishes dry wonderfully even without heated-dry, as the Miele DW pops the door open a crack, when it is done washing. That's all it takes to dry things.

M.....the Miele automatically opens the door a crack after washing?? If so, I LIKE that feature!

When we bought our Miele several years ago, this was a relatively new feature that was only available in their highest-end dishwashers. I think, these days, even a lot of the lower-end models can open the door. And yes, it's an amazing feature. It makes so much of a difference. The door only cracks open a few inches. But because of that, everything dries perfectly.

This of course works with any dishwasher, if you remember to manually open the door after the washing cycle. I often do that for the KA. I turn off heated-dry and then wait for the cycle to finish and open the door. But the Miele makes this so much easier.

If I have to remember to open the DW door to aid drying, I'd probably just hand wash my small amount of dishes! For decades, dishwashers have had a heat cycle. I never heard of any that ruined wood cabinets (and unless one had a steel St Charles kitchen, the cabinets were always wood, often painted). Were they vented differently in the past?

You don't have to open the dishwasher for the residual heat to dry the dishes. But if you don't open it, then you just have to wait a lot longer for the little fan to do its thing. Also, if you washed a load that had very little thermal mass, then there might not be enough residual heat. This is primarily an issue with plastic items, or with washing really small loads. Metal, glass, and ceramic usually dry just fine either way.

So, yes, you'll be OK with a modern dishwasher. As long as it has a stainless steel tub, there is enough heat retention to dry everything except (maybe) plastic containers, which will have a few drops of water still on them.

But if you have a dishwasher that does open the door, you'll find things just work nicer. The drying cycle completes much faster and even plastic items are typically try. Also, there is less chance of a high humidity environment inside the dishwasher for the next couple of days. That's a problem for people who only run one or two loads per week. The high humidity can foster bad smells. But if you do a load every day or two, then this is unlikely to matter much to you.

"M: As long as it has a stainless steel tub, there is enough heat retention to dry everything ..."

That is a common misconception about how condensation drying works. The stainless steel tub does not retain heat. The dishware retains heat. The tub cools faster than the dishware, which draws moisture off the dishware and onto the tub surface where it drips/runs down to the bottom (which is why there are sometimes complaints about the tub being wet at end of the cycle).