Thermal storage is great for any time of year

Situations differ.  Why keep an unoccupied room comfortable ?  Sure, enough to not freeze the pipes, but beyond that ?

I come in, turn on my window a/c (SEER 11 heat pump), strip quickly, perhaps take a quick "unheated" water shower (my NG is off and will stay off till October) and it is acceptable within a few minutes close to the a/c.  I keep the door closed to the front room so as not cool it.

More thermal mass just slows the process and keeps me uncomfortable longer.  And the temperature delta between inside & out shrinks when I am away with low internal thermal mass.

"Unheated" water in Austin, TX is blood-warm in July and August.

That's only true of environs so far south (and with very shallow water mains), though.  And if you were cooling by e.g. passively radiating heat to the sky at night, thermal mass would be the only way you could enjoy the benefits during the day.

Right, that's what I do.  use the fairly cool night to get my house down with an attic fan, then shut everything tight during the day, and use a little personal fan if needed.  Works great, and people think we have AC, which we never did.  But sure Alan.  In NO, that wouldn't work  As I remember, just hot and sticky ALL  the time.  So  I understood my thermo prof when he talked about heat death!  Been there.

But there are places in the US where the daily temp goes up and down like a yo-yo, and thermal mass can be used to great effect if you have the equivalent of a Maxwell demon working the in and out valves.  fortunately, yu can buy maxwell demons at radio shack these days.

The low this morning, just before dawn, was 81 F (27 C) with a dew point of 76 F (24 C).  This is slightly cooler than average for this time of the year.

Not much overnight cooling !