Should Motorised Valve Get Hot?

They do get quite warm but shouldn't get hot except when the pipe is hot. Since you had the valve sorted, call the person who repaired it.

Should zone valves get hot?

If you have a mid position valve - the one that makes a T junction, one pipe goes to the hot water cylinder (marked B on the zone valve), and the other to the central heating (A). The pipe marked AB comes from your boiler, so it should be hot.

Should a 3 port valve be hot?

This means that if heating or heating and hot water is the last service called for the valve holds in its last position still using the motor making the valve hot to touch, this is normal operation even if the system has not been operated recently and is how the valve has always been and is nothing to be concerned ...