Earlier quoted context omitted.
You might want to replace that core2duo with an ivy bridge laptop or a similar device, which you could find for ~£50 (maybe with a broken screen). The power consumption will drop by more than half. But if you don't run the system 24/7 then it's not worth it.
Funny you mention power as it was on my mind recently. The box hits 60w at full use so it is not a major concern. I would be more concerned leaving a laptop power supply on 24/7. I’m not sure if my concern is unfounded, what do you think?
A modern power adapter is at its core just a transformer and a regulator. Three transformer itself is a passive device, it's the regulator that will use a bit of power that will turn into heat, but any well built one will have no risk of overheating. The heat is proportional to how much power the laptop is using, (i.e. under how much load it is on average).
Modern laptops use very little power, so I'd say there is little cause for concern.