Actually not quite. Sunlight peaks when the sun is highest in the sky. That would be noon if not for daylight savings time and "time zones". So call it one o'clock, plus or minus a half hour. Peak temperatures are reached about 4 or 5, while peak air conditioning load is a bit later yet.
Ever hear of thermal inertia? The same effect occurs seasonally. The longest day is about 20 June, but the hottest days aren't until late July or early august.
I could write the partial differential equations that explain it, after consulting a text book (it's been a LONG time), but I don't think that would help you much.
I'm Ok with your "Actually not quite" part. My comment is mostly still applicable. More power is needed in the daylight hours. Solar power is generated in daylight hours. It is a natural fit...and STILL is not economic.
As for the whole Diff Eqns not helping me much...I took a LOT of graduate level Physics and Math for my Engineering Master's Degree...I'm not as dumb as I post...