Although it may seem hydraulic, I get the feeling its electrical and has to do with the switch in the top cover for the tranny you exchanged. That is all that is different between the two applications that I get from your post. I did not dicern form your post if the tranny switch or the operating switch inside the auto is new.

Power routes to the solenoid through the tranny switch so the OD is only available in 4th gear. The switch may be slightly gummy and slow to move when cold. The heat from use loosens it up then it works correctly from that time forward. It may be slightly worn on the end inside the tranny where it contacts the linkage. The top cover may be bent or slightly out of position. Washer between switch and cover too thick. Heat expands everyhing and all works and tests normal as you try to locate the problem.

A small test lamp wired with the solenoid where it comes OUT of the tranny switch to inside the auto then to ground will tell you what is happening to the solenoid power during that short period it acts up.

Duane