AT transmission issues

On my continuing quest to prolong my inherited 93 sonata's life I bring
you guys another issue. When the car is cool, aka not run for a while,
the automatic transmission works just fine, you wouldn't even know
there where any problems. However when it starts to get warmer and
used, the weird stuff starts to happen. The most prominent thing I
notice is that if I were to coast for a while, or even at a dead stop,
then hit the gas to keep going or in the other case take off, it seems
like the engine is out of sync with the transmission or there is play
in the line (as far as I know that's imposable) I say this because
there is a thud before the torque is transferred like it was not
engaged for a second and the motor was just free spinning. The other
issues I think I notice are when it shifts, its doing a little thud
when it goes in to gear and the shift point may be off, or I might be
making this up in my head. I know the first problem exists, any ideas
on what could be causing that to happen and what can be done to fix it?

 

Check the condition of you transmission fluid. If the level is proper and
the fluid is in good condition, chances are good that you're looking at an
expensive transmission repair or replacement.

 

It's beginning to sound like this car isn't worth fixing, unless he just
wants to use it to learn how. Sometimes a free car is a bargain,
sometimes it's worth exactly what you paid for it.