Sure, but how does the temp of the thermosphere affect the...

Sure, but how does the temp of the thermosphere affect the troposophere considering each layer is discrete? And so on down the layers...

The layers are not discrete. It's an airmass. Molecules and radiation are quite free to move up and down in altitude.

considering that the interface is nearly 100 deg C below zero?

Not really informative as I've already explained.