As far as I can tell:
The TMS tries (and is generally successful) in preventing the battery from exceeding 98 F, but it makes no effort to maintain some "optimal" temperature lower than that
I live in SoCal and I have never observed my battery cooled to the point (based on what I've read here, 50 F) where the TMS attempts to to warm the battery, but based on how it works at high temperatures, I would expect it to heat to 50 F and then stop TMSing.
So it looks like there is a window between 50 F (I am told) and 98 F (I have observed) where the TMS does nothing, simply allows the battery to go to whatever temperature circumstances cause.
Unless it's quite cool, the battery will generally progressively heat up to 98 F during charging, at which point the TMS system will prevent further temperature increases (perhaps a degree or so, I've never seen more)
Driving will heat the battery but not nearly as fast as does charging. I can go on a 40 mile freeway drive with the battery starting at 70 F, and when I arrive it will have warmed only a few degrees. If I plug in and start charging, and it quickly starts climbing. If I don't plug in, temperatures remain quite stable. Even on a hot day, it will climb slowly until charging begins at which point it will heat quickly.
This design is different than, for example, in the Volt. People have shown that the Volt TMS system keeps the battery between approximately 85 and 70 F when plugged in a not charging. It is what the NREL calls an "agressive" cooling system. The FFE does not work this way as far as I can determine. It simply keeps the battery temperature from exceeding the limits of 50 and 98 F. I don't know how Tesla/Toyota/Mercedes or BMW work.