I have a 1992 Dodge B250 Van with the 5.2L V8 and a Mopar A727 3-speed transmission that jerks/kicks when I give it gas from a stop, only after it has warmed up. When it is cold there is no issue. The transmission shifts fine and there is no abnormal play in the driveshaft. I also do not think it is the engine because the engine revs up almost like it is in neutral for a second and then it roughly engages. This only happens if the van is warmed up, like after driving on the interstate for a while. Is it the torque converter? Or maybe the transmission?

 

you need to scan it and see what pending codes you have....is the check engine light on?
Neural fall out can be from a few things...a weak pump in the trans, bad communication (either cable or electronic), and clutch plates that have had enough and have no more friction material
Also your bands may be out of adjustment...these issues on 30+ year old vehicles are ones that you should not 1see 2see fix...you should pull the pan and see if you have the friction material in there...
what I am saying is you probably have never adjusted the bands, the TV cable, the valve body, and fluid have probably all be neglected. You have to address all of these things if you want a reliable van