Can a home be designed to specifically "retain heat"? Assume you have two identical bodies at temperature $T$.  One is subject to an environment characterized by a temperature of $T+\Delta T$.  The other is subject to an environment subject to a temperature of $T-\Delta T$.
Let $\dot Q_{1,2}$ be the rate at which heat flows from the object to the environment in two cases.
What mechanism, if any, would the rate of heat exchange in the first case not be the same magnitude, i.e. $\dot Q_{1} \neq -\dot Q_2$?
Suppose that in addition to the general ambient temperature of $T \pm \Delta T$, there is a separate stream of black body radiation with temperature $T_s >> T+\Delta T$ illuminating the objects under both conditions.  Let $C$ represent the rate of heat flow from the object when the local ambient temperature is $T$.  With this addition, is there a way for the magnitude of the rate of heat transfer to the local environment to differ?  I.e. $\dot Q'_1 + \dot Q'_2 \neq 2 C$?
 A: One way to keep a house warm (from a warmer day into the night or from human activities that generate heat) is to increase thermal insulation. Nature requires the thermal conduction of passive materials to be symmetric. However, the material property of thermal conductivity depends on temperature and thus can be asymmetric for temperature excursions above and below the nominal house temperature.
One can also increase the heat capacity of a house to buffer temperature swings (such as nightly cold conditions). Unfavorably, this would tend to prolong heat-wave effects inside. The heat capacity is also temperature dependent, also potentially leading to notable asymmetry. For example, the heat capacity of water during freezing (or any material in a first-order phase transition) is infinite; freezing and accumulating layers of slush during winter can provide cooling during the summer. Conversely, the opposite strategy (storing warm water for the winter) is not effective because the sensible heat is much smaller than the latent heat.
An asymmetric way to keep a house warm is to absorb as much sunlight as possible in the visible-wavelength range and reradiate as little as possible in the infrared range (e.g., from southern-facing windows in the Northern Hemisphere, to obtain a greenhouse effect). The analytical framework here is that the radiative emissivity $\varepsilon(\lambda)$ and transmissivity $\tau(\lambda)$ depend on the wavelength $\lambda$; bodies of different temperatures radiate different wavelengths, and transparent materials transmit different wavelengths with different efficiency.)
Another asymmetric mechanism relies on apertures such as windows that can be opened and closed as desired (or turned into insulators, as described in the comments), depending on whether one desires convective transfer with the outside. (You've since edited your question to exclude this mechanism.)
