TURTLE wrote:

The location is Texas, where the temperature is about 75 F at night
a nd 100 F at the hottest part of the day.

About 88 average over 24 hours, and about 82 at night...

If you turn a hvac system off less than 8 hours. It will cost you more
money to recool the house from a very high temperature to the lower
temperature than just moving up to a higher temperature on the thermostat.

Well first I see you don't work on hvac system and know what the run times are
for a properly sized hvac system verses a cool down time for a indoor temp. of
about 105ºf down to 70ºF to 75ºF.

How would the house get from 70 F to 105 F in 8 hours on a 100 F day?
Assuming it could (which would save lots of AC energy), and assuming
it had resonable insulation, it would have very little thermal mass,
so the AC could cool it back to 70 F very quickly.

Now if you have oversized hvac system like 5 tons on 1,500 sq. ft. house.
Your answer would be ok, but a properly sized system would cost you big
time on a 4 hour down time.

The setback would still save energy, unless the AC becomes a lot less
efficient (has a lower COP) with a higher indoor-outdoor temp diff.

A 1500 ft^2 house with 300 Btu/h-F of thermal conductance could warm from
70 F to 105 F in 8 hours on a 110 F day if RC = -8/(ln((105-110)/(70-105)
= 4.1 hours, which makes C = 4.1x300 = 1200 Btu/F, not much. A 36K Btu/h
AC might cool the house from 105 to 70 F in (105-70)1200/36K = 1.2 hours.
Keeping the house 70 F for 8 hours would require 8(110-70)300/36K = 2.7
hours of AC operation... 1.2/2.7 is a 55% energy savings.

Nick