I leave next week and the weather will be hotter than I anticipated

My route is not set in stone but I plan to drive from Tokyo to the Nagano area for a couple nights and then on to Toyama.

From there I will do a 2 night stop in Osaka before continuing on to Kochi and the Setonaikai National Park, Eventually I will make it down to Fukokua.

If any Forum members have any suggestions of must-see tourist sites or over-the-top accommodation or experiences in these areas of Japan, would to hear about it.

I am also really interested in possibly visiting vintage shops and flea markets.

Just curious as to why you are driving. I assume costs are not an issue? As for heat, August has always been very hot and recent summers have been significantly hotter than “normal”

Shinkansen to Nagano visit Zenkoji
Get car and go up into the mountains for hot springs, maybe snow monkeys
In Toyama prefecture, have black ramen a local specialty. Visit nearby Kurobe Gorge.
drive south via Takayama or better with a car go via Shirakawago and Gokayama
best is just to take the trains from Toyama to Osaka
train to Okayama and get a car to head to Shikoku which is a good place for a driving visit
when you get to Shikoku side of Seto Ohashi find the viewpoint back to see the bridge system you just drove across.
drive back to Honshu via Seto Nai Kai NP, maybe stop in Onomichi
leave car in maybe Hiroshima and shinkansen to Fukuoka

It is suboptimal to start planning a trip with only a week before departure.

excellent recommendations but there will be zero 'Shinkansens'

I will pick up my rental car at Haneda and return it there 3 weeks later

this way I can visit any place I like along my route

I hope you will not be crossing multiple time zones before reaching Haneda. If you are, you will NOT be safe to drive -- not safe for you, not safe for anyone else on the roads. You'll need at least 36 hours to adjust. Any one who says it'll be fine has just been lucky.

lol
One week before you leave and your only starting to plan now? Please let us know how it all turns out when you get back. Good luck!!