Yes under clocking the CPU will cause it to produce less heat. How much you need to under clock it is impossible for us to say. Keep clocking it down and testing under load until the heat sits in a range you're comfortable with.
Having said that, it's not the processor being faulty that's causing overheating, it's your cooling apparatus.
Since it's a notebook, it's probably got at least one heat-pipe, and if that heat pipe is fractured it won't work properly and heat will build up, regardless of how clean the vents and heat sinks are or how fast the fan is spinning.
Fractures in a copper heat pipe can be near impossible to see with the naked eye, and if they happen on a seam it will make it even harder to spot.
Replace the entire cooling apparatus (heat sinks, heat pipes, and thermal paste), which usually comes as a single "part" from the manufacturer.
To find the right part(s) contact your notebook's manufacturer and ask them to locate you a local repair depot. Contact that repair depot and either get them to fix it, or see if they will be kind enough to order the part for you.