Any question answered...

Dismantle and new heat transfer paste between the heat sinks. Actually clean the blades of the fan.

Don't blow compressed air into the vents.

A small computer shop wouldn't charge much to open it up and clean it out if you don't have the confidence to do it.

It sounds like you're not even sure what the problem is, overheating is just a guess? Instead wasting a lot of your time, probably pointlessly, get someone else to do it. It's amazing how many people say their laptops overheating and shutting down, when usually its a faulty HDD or something

Thanks. Going to take it to the repair shop.
Another question then - Can you recommend a place in London?