Good! You have probably sorted it. Heat link terminals are in a tight space and quite fiddly, even for those of us that have had a bit of practice. It's not uncommon to find a bad connection.
If it has been working correctly, then most likely the wiring will be correct. However, if "after pushing cables" things change I would start with checking the connections are secure and that the metal wires and not the outer insulation are in contact with the terminal screws. Having said that, loose wiring usually means things don't work when they should, not the other way around and come on when they shouldn't do.
When the heating stays 'on' when it shouldn't be 'on', is the Heating light on the front of the Nest Heat link lit?
View attachment 209251
If the light is on, then the problem is with the Nest, or its settings. If the light is going off but the heating remains on the fault is elsewhere.
It won't be the boiler. Its sole task is to produce heated water when requested. The motorised valve and controls switch the boiler 'on' and then direct the aforesaid heated water to the radiators and hot water cylinder as required. It may be that the motorised valve isn't closing the heating port properly when it should, especially if it's a bit stiff after a long summer rest. In which case, when the hot water is operating, water will also go to the radiators as well. With the heating and hot water both 'off' try sliding the manual lever on the side of the motorised valve a few times to see if it frees it.
Unless you are using gallons of hot water constantly, the hot water cylinder should heat up quite quickly say 10-30 minutes depending how cold the water in it is to start with and then the cylinder thermostat will shut it down, so I wouldn't expect it to make much of a difference to your gas consumption and the short on period is unlikely to make the house "extra warm".
Over a forum this sort of thing can be difficult to diagnose. However, the person servicing the boiler should be able to fault find for you quite quickly.
If you're sure it's the Nest and have tried a restart already, the only other thing I can suggest is a full factory reset. This will erase everything and take it back to the condition in which you originally received it. If you want to try it you can find the instructions here.
If you're sure it's the Nest and have tried a restart already, the only other thing I can suggest is a full factory reset. This will erase everything and take it back to the condition in which you originally received it. If you want to try it you can find the instructions here.
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