Hello Jim,
The engine, transmission and cooling system related parts have no built up heat in them when you start out to your cruise nights, but after the drive to the event, you now have large cast iron parts with internal heat built up in them and on the drive home your cooling system is not handling the heat exchange properly, so the temp gauge will reflect that. Below are a few things that I'd look into first.
(1) Are you running a 180 / 185 degree thermostat and the correct mixture of anti-freeze and water recommended for the weather temperature range in your area? I can tell you from personal experience, that running a 160 degree thermostat on a street driven car does not help to cool down a warm running engine and that running a coolant mixture with too much anti-freeze, or to much water will affect engine operating temps as well, especially in the hot temperatures like we have here in Phoenix AZ in the summer months.
(2) Another thing to check that I've had happen to me in the past when I was still using factory style rubber radiator hoses, is to make sure that your upper and lower radiator hoses (usually the lower hose) aren't needing to be changed due to age and heat cycles, which will allow them to weaken and pinch partially shut and restrict coolant flow when your cooling system is under pressure and up to normal operating temperatures. I switched over to running the seamless copper "Cool-Flex" radiator hoses on my 66 Coronet 500's 440 and my sons 72 Dart Swinger's 318 and have eliminated
all of those troublesome rubber radiator hose issues on both cars. They don't look factory stock and they are more expensive than rubber hoses, but you purchase one set of them for each car and they will be the
last radiator hoses that you will ever need to purchase for that car. The ones on my Coronet have been in place since 1991 and still look and perform just like they did when they were installed and the ones on the Dart have been in place since 2005 with the same excellent results. Have a 100 point show car? Use factory style rubber hoses, but for anything else you want to actually drive, check into the Cool-Flex hoses. I use the chrome plated versions, but these also come in Black, Red, Blue and Purple as shown in the following pictures.
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The end cap covers come in different finishes and colors also and as you can see in this picture below, this seamless copper hose is extremely flexible and will stay in whatever shape you need for your application.
(3) If your Coronet has an automatic transmission, is to make sure that the transmission fluid level is topped off to recommended levels. This is important for many obvious reasons, but many forget that on a factory set-up, the transmission fluid is cooled by running it through the lower radiator tank, so if the fluid level is low in the transmission, it can build up extra heat in the transmission which will be transferred to the radiator, which will be transferred to the radiator coolant, which will then be transferred to the engine and so on and so on. On my sons Dart, I've installed a properly sized aftermarket "bullet" style transmission cooler up front in the opening of the lower valance pan and just behind and under the front bumper. This location gives the cooler an unrestricted source for fresh air to flow over the coolers aluminum fins whenever the car is moving and also provides a nice air gap on all sides of the cooler to dissipate heat even when the car is sitting in traffic. Along with this new cooler, I also removed the original factory transmission fluid lines and replaced them with custom made new steel lines that direct the transmission fluid completely out of the lower radiator tank and directly to the new cooler, so all of that previous heat from the transmission fluid is no longer an added cooling burden on the radiator to handle and it also helps to reduce transmission fluid heat build up. This set-up fits like a glove in this location and almost looks like a factory option and has worked out so well on the Dart, that I will be doing a similar system on my Coronet in the future.
Here's a couple of pictures showing the transmission cooler right after it was installed during the cars restoration back in 2005 / 2006 and a shot of the front of the car showing the coolers location with the lower front valance pan and front bumper in place.
(4) One last thing that I'd check, is your engine timing, as if that's off, that will affect engine operating temperatures as well.
You have some fantastic cars there Jim, so I hope you figure out your Coronets cooling issue soon and not have to worry about it any more.
Richard