Hyundai Repair: error codes/transmission, tiburon hyundai, solonoid

Question
car-- 2000 tiburon.hyundai
error code P1624--cooling
error code P0734--4th gear ratio
The first doesn't really concern me, the second does, at high speeds is bucking/hesitating
This is my daughters car, she took it in for diagnostic, and they said trans needs rebuild,
I don't believe this is only 67K miles
I have worked on cars for over 30 years, is there something I can look/do to find the exact problem,
a sensor, a solonoid? Any assistance would be appreciated.Since I am an old timer, I understand things have changed, but last time I was told I needed a new/rebuild of trans.,, was a 71 fury, fixed that problem with new spring and poppit,on the hydraulics, was just hanging, ten minute fix.
Thanx,
Tom

Answer
As you have stated an it's not i saying this ,that was a 71 an this is a 2001.  the inner workings have come some way an since then to now computers run everything an to get a trans to work the way people want them to work today the inner workings are a lot different then you think they might be,so yes I would have to say trans is shot an needs to be redone sorry to say,this is do to the way trans shift today they must sliip to have soft shitting so this is why you must always have service done every 15k so keep the fluid so the trans don't do this.so once again sorry to say trans is shot.