The rate of heat input reaches its lowest at the solstice. However for the next month or so that rate does not rise sharply. Through January, although rising, it is insufficient to stem net cooling. It is only later that the amount of insolation reaches the level required to stop net heat loss. In the late summer the same principle applies - although insolation is falling it still exceeds heat loss so the temperature continues to rise -although it slows - and then goes into reverse.
There are other damping affects (eg sink effect of the sea) but the main factor is that the land temperature does not depend on the rate of change of insolation but rather on whether insolation is greater or less than radiation.