Mopar Muscle Association UK

Its deffo your cable have had this a couple of times after first buying cars did Daves trick he presto problem sorted (listen to uncle Dave)

I agree,
When the cable cools and its red outer sheath is cold you can get the cable to release inside, the once hot outer sheath.

This will get worse until its "Cattle trucked"

Route it again, as far as possible and fit some heat shield sheathing over it or header wrap works.

Mine wasn't sticking in the cable. The cable was getting longer. With the selector length on the long side as well it just made things worse.

One of these days i will take the selector lever off and weld/re-drill it.

Dave mine stuck fast...took an hour to free it off....knackered the cable.

I've never doubted your opinion before Dave but would the cable length really change by enough to have any effect?
You're not even heating the whole cable, just the short section next to the header. In addition, surely the sheath AND the inner will be heated pretty equally and will therefore expand equally, cancelling any expansion effect.
One effect of heat on a cable i've experienced is the plastic inner sleeve swelling and gripping the cable, reducing the movement at the far end until ultimately it seizes completely. This eases once cool but never fully recovers.

I'm pretty sure the cable wasn't sticking. But it wouldn't pull back enough to go into park when hot. If you adjusted it so it went into park OK when hot then it wouldn't go into 1st when cold.

Maybe I'm wrong. You explain it.