In fairly cold weather (10-20F), the car starts and can be put into gear but
the accelerator can't be depressed (seems to be stuck - but it's not).

Then, when the accelerator is FIRMLY depressed - or the car warms up - the
transmission won't shift out of first.

When the car gets fully warmed up, everything's normal.  It is
temperature-sensitive, for sure.  I drove it at 38F with no trouble, once it
warmed a bit.

Thinking it might be low transmission fluid, I had it flushed and refilled.
Still have the problem.   Could be the shop didn't fill it per spec, of
course, but I did check the dipstick before the engine was fully warmed up
and it seemed like there was plenty of fluid in there.  Too much?

The one other thing that's a tad weird - as it idled on a cold day, the car
heater worked just fine.  When I got it out on the road, though, cold air
started to blow from the vents.  Engine temp guage rises to normal and stays
there.

Any thoughts?