Are you sure they're transmission lines and not oil? The setup on my '93 SSEI is coolant and oil are cooled in the radiator and the transmission has its own cooler. This won't matter anyway because the thermostat only controls when the COOLANT (only used on the engine) is let back into or out of the block. This whole thing is a cycle. Your coolant starts at your radiator and at a certain temp your t-stat opens up and lets that coolant in. In the meanwhile you have coolant that was in the block warming up to that temperature. As the t-stat opens cold coolant from the radiator comes out and the hot stuff goes in. Now that the block has cool fluid the t-stat closes again and the cycle repeats. Now if you don't give that coolant in the radiator enough time to cool down below the t-stats temperature your t-stat will just stay open and it will flow in a loop slowly warming itself up until your fans kick in and cool the whole thing down. Thats why your car still runs at normal temps when you sit still and runs cool when your moving. Your radiator doesn't cool it unless there is air blowing across it. No air and it gets hot and holds the t-stat open and now you've got a cycle that would overheat your car if not for your fans. Hope that clears a few things up