Surely the day before the solstice is warmer than the day before the equinox. But the solstice is not the hottest day of the year.
Nor is noon usually the warmest time of day. 3:00 PM is generally warmer. There is approximately a six week lag between the solar driving function and the effect on local weather, as the oceans warm up.
The total amount of sunlight in the northern temperate latitudes between the March Equinox and June Solstice is about the same as between the June Solstice and September equinox. June receives more sunlight than July, but July is warmer. Likewise, December receives less sunlight than January, but January is colder.