Wintertime temperatures in the SE US are largely coupled to baroclinic zones and their associated airmass exchange and advection between the mid and high latitudes, while
the airmass over the SE US in the summer is typically humid-tropical, quasi-barotropic (i.e. only dependent on pressure variations),
and characterized by an absence of fronts, hence temperature anomalies are primarily dictated by precipitation and concomitant evapotranspiration from the ground, vegetation, etc. Also consider the Clasius-Clapyeron equation, wherein saturation vapor pressure (saturation vapor pressure is essentially equivalent to saying when the air reaches 100% relative humidity (RH) for a given temperature) is a function of temperature alone. Note that saturation vapor pressure (usually expressed as Es) increases exponentially wrt temperature and that water has a specific heat capacity that is ~4-4.5x that of the air. Therefore, it takes significantly more energy to change the temperature of an airmass with the same relative humidity in the summer as it does in the winter. Hence, we can conclude the combination of a dearth of fronts and warmer temperatures promulgating higher ambient vapor pressures contribute to the relative lower variance of summer vs winter temperatures in the southeastern US.
Here's a graph I plotted using the C-C equation w/ saturation vapor pressure over ice and water to show you the non-linear relationship between the moisture capacity of an airmass (saturation vapor pressure) and temperature
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