Have an old Honda VT 500 E Motorcycle. Seems that the regulator / rectifier becomes very hot in working condition. Also the voltage is a bit?

To high: probably 14,6 V. After engine stop the battery is overloaded.
My Question is additional cooling can be a solution or not?

Added (1). Measured with a DMM for certain!
&
Battery is 14 Ah lead-acid battery

Added (2). Is a new Battery and 1 stage bigger than the original; instead of 12 Ah it is 14 Ah one. And no all cells are ok, after charging the Battery has 12,8 V and keep this voltage over the time.
Regulator / Rectifier is already with finns and i mean i can always touch it with my hands. Therfor the temperature isn't over 50° Celcius at the finns.

14.6 output is quite normal to overcome the resistance of the battery. However those old Honda rectifiers /regulators are notorious for failing so replace it with a new unit. They aren't expensive and you should look for a finned version that helps to cool it down. They are simple to fit… Just unplug it and undo the retaining nut.

A very hot regulator is oindicartive of maybe a shorted nattery cell. EWhat does it read, nmotypor off, aftyer a couple hours> 10 volts> BNew Battery,

Otherwise, a hot rec/reg can be indicative of an open or intermittent rectifier diode. The others have to work harder. A shorted diode is cool. I had a Chinese replacement one with intermittent diode, when it made contact, cool and fine. Bad connection Hot. This means New rec/reg unless you want to dig into the potting epoxy and find new diodes. On EBay. Get a used but good unit, about $34

An 14.6 output is reasonable, ride with light on. I worry at higher then 15 Volt. The battery charges up to 13,2 Volt but can go beyond when new. Batteries seem to settle at 12,8 Volt for a larger amount of time then 13,2 and 13.

Fins at regulators do not help much as the components are embedded in rubber paste and do not toch the mantle. Nevertheless manufacturers of motorcycles mount them on the frame where it is flat and not painted. Do not change a winning team. Cheap regulators may have other components. Regulators fail when the contacts on their plug or the plug for lengthening the cable fail so that is the thing to maintain and check.

Your regulator is not hot but it seemed to be? They short their overload back to the dynamo and can get warm.