In that case, the only option is to use the laptop on the power cable all the time. As stated before, blow the fan out with a can of air, and make sure it is actually spinning to cool the CPU.
Use a can of compressed air to blow any potential dust out of the fan. Make sure the laptop is off when you do this.
The battery needs to be replaced, bottom line.
What kind of Laptop do you have? Brand, model?
I'm having an issue with my Logitech G930. It has been happening from the time that I bought it, and reaching out to logitech has resulted in no solution. I even went back and exchanged it to see if it was a malfunctioning headset.
The issue is that while I'm listening to audio through them...
Windows 8 hard codes the product key into the motherboard itself. Switching HDD's is fine, it will pull the product key information from the mobo and activate like normal. Enjoy the SSD!