I would guess your grass is mostly Kentucky Bluegrass.  When temperatures reach the 90's and we have an extended heat wave, it tends to go dormant.  The fact that the shady areas are fine probably proves this.  Additionally, soil on top of clay forms a layer effect.  Originally the top soil should have been tilled into the clay along with a large amount of compost.  Right now it is like some soil on top of a cement base.  Try aerating your lawn followed by top-dressing with quality compost to lessen compaction and add organic matter to soil. This will improve water infiltration in heavy soils.  Also a light sprinkling every other day does nothing to encourage deep rooting of your grass.  You should put down at least an inch each time and allow the water to soak in.  Once a week or so should be enough time for this.
Keep the grass at least 3 inches in height.  You are mowing it too short.  Good luck.  I know it is frustrating but try these options.

Thank you for your prompt reply today. 

I am familiar with your recommendations, most of them have been deployed, aeration in the fall the past 11 years, except last, top-dressing applied in worst areas. Applied new seed last fall (with tested resistance success to drought, again four blue grass species) which I thought would need more frequent watering. Can adjust to once a week with longer station run times. Additionally we have tried some dormant seeding the last two winters. We are scheduled to aerate 2nd week of September this year, with a "seed soil" top-dressing in preparation for fall seeding. The last 4-5 summers we have mowed to the 3 inch height, but with the same 3x per week watering accumulating to the one inch per week.

Can you recommend a person, a source, or path to determine or eliminate the possibility of a fungus? 

I am sending in a soil sample from the affected areas, There a number of analysis options. Which ones would you recommend? 

Thank you again for your prompt comments, 

Mike

Without actually seeing the grass personally, I cannot help you with a diagnosis.  However, I am giving you a link to a fantastic source at Michigan State.  As you click on the various choices it will bring up details.  
Turf Diseases - Turf (msu.edu)
I don't know where you were planning to send your soil sample, but soil samples do not test for disease but rather fertility: 
Lawn & Garden | Soil Testing Laboratory (umn.edu)
If someone were to look for a problem with your turf, they would need a square foot of turf with half of it the dead grass and half where the grass is still alive.  Once grass is dead there is no green so no way to see what happened unless it is something like Rust which leaves rusty powder on your shoes.  There will be a Master Gardener Booth at the State Fair in the hort building.  You could bring your sample there.  You also could try to bring a sample to a locally owned full service garden center to see if someone there would be able to spot your problem.  You could also try contacting the Hennepin County Master Gardener office to see if they have a plant health clinic where you could bring your sample:  Phone: <personal data hidden>

After all this, I still believe your problem is the combination of the weather and Kentucky Bluegrass.  If your lawn greens up as the weather cools, that will confirm.  I know this is frustrating but I do not know of any company who has personnel who come out to diagnose.  Unfortunately, most of these companies just come out and spray fertilizer and weed killer at set dates without any expertise.