We have recently acquired a '96 Dodge RAM B2500 Conversion Van.

Since winter came around it developed a strange problem just after starting - if we try to put it into reverse with the transmission cold it would sit for around 40-50 seconds doing nothing then it would "bump" hard into gear.

With the AT fluid hot everything works as it should, the Reverse engages smoothly as soon as we move the lever.

Any idea why this happens and how we can fix it?

 

That is the symptom of your low/reverse band about to fail. You can try changing the filter and adjusting the bands but personally I'd start pricing transmissions.

 

You might be due for a fluid/filter change and at the same time the low/reverse band should be adjusted. In the meantime, first shift into Drive for a few seconds, then shift to Reverse. Shifting into Drive gets the fluid pumping through the tranny faster.