A bad or corroded post on the dist. cap for cyl #3. Carbon tracking in the cap or even a hair line crack in the cap. A cold engine runs richer which in my experience will sometimes mask a weak spark or low compression until the engine warms and the mixture then leans out. A break or bad connection in the injector harness. With thermal expansion maybe a problem in the injector circuit occurs as the harness gets hot from a hot engine. Then there's still checking for a plenum (vacuum) leak. These are a common problem on Dakotas with the Magnum engines 3.9, 5.2, 5.9. Look down the throttle body for any oil pooling in the manifold. Spray carb cleaner around #3 cyl. for an indication of a vacuum leak.

I had a car that ran fine when cold but when warmed up would have a dead miss. Eventually removed one of the heads after a hot compression check revealed low compression on one cylinder. Compression was normal at a cold crank but after the head heated up a crack between the intake and exhaust valve expanded enough to kill the cylinder. I hope it's something simple. Just remember that heat cycles themselves have an effect on every component under the hood.

Installed new distributor cap and rotor, no help.
Paper test, no obvious in -draw on exhaust.
Starting Fluid test, no obvious signs. Sprayed injectors, throttle body area, header area, nothing got thru.

Like a single beer fart, you can hear the mis at idle.
GRRRrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr!

Try swapping plug wires with another cylinder just to check and eliminate another possibility.