1998 new beetle 2.0 gas automatic transmission

The somewhat football shaped "transmission cooler" on the trans with 2 hose connections, what goes in and out of it? Does engine coolant flow through it into the transmission or does transmission fluid flow out through the radiator?

The fluids are mixing and i was wondering if i can just run the hose from inlet to outlet and basically bypass the trans cooling until I have the time and money to fix it right.