[GistNoesis]

I find the idea of reversing the air flow direction every 30s simpler to understand than two counter-flowing pipe side by side.

Imagine a pipe filled with 3 metallic grid sections (such that the air temperature in the section will equalize with the metal temperature) separated by plastic grids (such that the heat isn't conducted through the metal), and you push air alternatively from one hot side at 20°C to a cold side at 0°C for 30s and in the other direction for 30s.

For symmetry reason, the pipe will passively (we don't count the energy required to move the air) have a gradient of temperature from the hot side to the cold side. The first section will be ~15°C, the second ~ 10°C, the third ~5°C. (Each section temperature is the temporal average of the temperature of the air flowing from previous sections : so because air switch direction, it means it's the average of left and right sections.)

From the point of view of the house, you only lose energy from the first section of the pipe which will be more like 15°C rather than 0°C.