To All:
Distributors normally don't run hot.
Even when the engine over-heats, the location of the distributor, up on a relatively cool corner of the crankcase, combines with the heat-flow path and the ratio between the neck of the distributor and its body, to cause the distributor to run significantly cooler than the crankcase.
So if you have a hot distributor it's a pretty good sign that something is wrong ...and that 'something' is usually that your engine has been improperly assembled.
Have you got a distributor handy? If you'll examine the neck of the distributor you'll see a hole drilled into the neck just below the groove for the O-ring. A machined trough runs from the hole to the bottom edge of the neck. As you may have guessed, the hole and the trough are there for a purpose, which is to lubricate the shaft of the distributor.
Grab a crankcase and peek down inside the hole where the distributor goes. On the uphill side of the hole -- the side nearest the center-line of the crankcase -- you'll see a small window cast into the side of the hole. When the distributor is properly installed, the trough on the side of the neck of the distributor connects with that window. Of course, that only happens when the ENGINE is properly assembled, since the orientation of the distributor's pinion gear dictates the installed orientation of the distributor. (On the pinion gear, the slot for the dog-gear must be perpendicular to the center-line of the crankcase when the #1 cylinder is at 7.5 degrees before TDC. The smaller segment must be toward the pulley. Note that the alignment is for the STATIC FIRING POINT and not TDC.)
Notice that the window opens onto the cast 'shelf' that serves to align the thermal insulator that isolates the fuel pump from the crankcase. The angle at which the distributor is installed and the location of the shelf combine to provide a constant supply of oil for the distributor shaft. Install the distributor incorrectly and you've just shut off the oil to the distributor-shaft bushings. And while the distributor shaft only rotates at half the speed of the crankshaft, it still needs a drop of oil now & then.
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Back in the Good Ol' Days -- whenever that was -- it was pretty rare to run into an improperly installed distributor. Nowadays it's become pretty common. Why? Mostly because incompetent mechanics install the distributor's pinion gear incorrectly. Which leads to plugging in the distributor so that no oil can get to the oiling trough.
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Gotta hot distributor? Then there's a high probability it's been running without adequate lubrication. So fix it. Bring the engine to the firing point on #1, pull the pinion gear (you'll need the special puller) and re-install it correctly, making sure to provide the proper number of shims.
How common is this problem? I wish I could say it was rare but about HALF of the engines I see have the distributor drive-pinion off by one or more teeth. Which is a good reason to send the fellow on his way, at least here in the Peoples Republic of California. Because as soon as you lay hands on the thing you can be held liable for ANY future problems. (You don't have to pull the distributor to see that it is mis-aligned.) Installing the distributor's drive-pinion incorrectly is good evidence that whoever assembled the engine doesn't know their ass from their elbow, meaning there's liable to be other, less visible problems, such as mis-aligned bearing shells, wonky valve train geometry and even a mis-aligned cam gear -- all of which they will lay on YOUR doorstep since you were the last person to work on the vehicle.
So you smile, praise their paint job or upholstery or some damn thing, and tell them you're too busy right now and wave them on their way.
-Bob Hoover