Most HVACs thermostats have a target temperature range and can toggle heating and cooling to stay within that range - usually with some minimum range logic to prevent constant swapping.

This is also a classic modern house problem. In areas with wild temperature sways like what you’re describing traditional house building would include hacks to capture and retain the cool air in the morning and shed as much excess heat as possible during the day.

When we lived in Puerto de la Santa Maria we’d throw open windows to create a cross breeze in the mid afternoon and keep the air flowing (assuming it didn’t get too cold) into mid-morning at which point we’d seal off the east facing windows and draw curtains over the windows and doors to keep the heat out - swapping to full enclosure as it got to just before lunch time - then opening east facing windows and leaving the west shut util it was time to start the cycle again.

It was unbearably hot in direct sunlight during the hot months but the house stayed cool - especially with thermally conductive tiles and stone being the primary exposed surfaces. As long as you properly cycled the house you could keep it comfortable and it was easy to adjust by airing it slightly less or letting more heat in.

Wooden houses with huge sliding glass doors in direct sunlight that have no shades or curtains can’t do this, however.