Co-current flow (both flows moving in the same direction) work the way you described.

Countercurrent-flow heat exchangers (where the two channels of the fluid/gas) move in opposite directions on both sides of the heat-transfer mechanism maintain a heat flow gradient over the entire length of the heat exchanger. This can result in an almost complete transfer of heat from one current to another.

High efficiency HRV/ERVs use counter-current flow heat exchangers.