The reason that the daily maximum temperature occurs later than noontime is due to a delay between the max in the incoming sunlight intensity (yellow line) and the max in the outgoing terrestrial IR radiation rate (red line). This diagram shows that the outgoing radiation peak is only a little bit after the insolation peak, but it's significant. Also note that the outgoing radiation is never zero, since any object with a temperature above absolute zero (0 Kelvin) will radiate (Stefan-Boltzmann Law).

We recall that if the amount of radiation absorbed by an object is not equal to the amount emitted away, the temperature will change (see radiative equilibrium). Between a time shortly after sunrise at 6 am and a time in the middle of the afternoon, incoming sunlight intensity exceeds outgoing radiation rate, so temperatures increase. Temperatures increase until this relationship reverses in the middle of the afternoon, when the outgoing radiation rate begins to exceed the incoming sunlight intensity. This marks the time of the maximum temperature. From this point until a time just after sunrise, the outgoing radiation rate exceeds incoming sunlight intensity, so temperatures decrease. The minimum temperature is then reached at that time shortly after sunrise.

Note that the points where the max and min temperature occur are when the incoming and outgoing curves intersect, because that's when the relationship between the incoming and outgoing radiation reverses.