By power supply I actually meant the connector into the laptop. I had a Toshiba laptop and the adapter went into the side of the computer and one night the plastic inside the laptop broke so the connection disappeared into the laptop casing. It was simply remedied with a little superglue and it runs fine for work stuff but these are the little things that you have to be aware of when buying certain brands.
The only sane advice I can give to you is find a laptop that you like the look of and then find reviews for it. Two laptops with exactly the same specification can run in very different ways, this is because laptops are by nature little heat production units.
An overheating laptop is usually a very simple dust problem, if you do not feel confident fixing it yourself, it will be much cheaper to take it to a repair shop than to buy a whole new laptop. As your laptop is only two years old it may be able to be upgraded too, this will also be cheaper than buying a whole new unit and you can ask the repair shop for a quote on an upgrade.
I highly suggest a cooling fan, it doesn't necessarily have to be expensive or fancy, the point is merely to create a good airflow. A good airflow will actually extend the life of your laptop because overheating the parts inside is never wise.
Kindest Regards
KJ