Classic symptoms of overheating. It is a bit old, so heatsink is viable to be clogged. Best way to check: locate grilled exhaust of the cooling system and when computer is on and cover it with hand or piece of cloth. After 10 seconds or so (tops) the hand/cloth should get very hot and fan should spin up to max speed and be quite loud. If you feel only warm on hand/cloth, that's it.
Do the following:
- Shut down the laptop, remove battery and vacuum it as best as you can. I recommend using a soft brush end for that. GENTLY!! Concentrate on keyboard and every opening on the bottom and sides of chassis, taking extra time with exhaust. Again: GENTLY! Brush can get momentarily stuck under the keys and/or in the intakes, so slow and easy does it.
- Invest in a can of compressed air. Spray the air into the grilled exhaust. Spray the air into the fan intake on the bottom of the laptop. Repeat as long as dirt comes out of either end (and, quite possibly, from under the keyboard, so keep laptop open). I found out that this procedure works better with laptop turned on. You may end up using full 300ml can...
- If no dirt comes out either end you need to disassemble the machine and clean the heatsink/fan directly. In that case make sure you follow directions as in other answers.
Make sure you hold the can upright with valve on top, as compressed air turned sideways or upside down is used for fast cooling, which causes any sprayed surface to be moist.
When working as DELL DSP I often pulled dirt out of heatsinks. Sometimes they were closed with half an inch thick dirt, hair, thread and dust, compressed into one big layer, closing completely air circulation.
EDIT:
Cleaning heatsink/fan means that you need to disassemble cooling system into separate parts, as the dirt will build in the space between fan's prop and intake of the heatsink
Unfortunately there may be instances when cooling is clean. In that case there is BIOS update in order (if there is newer version) or in extreme cases fan and/or heatsink and/or fan control chip happened.
Those extremes require part replacement. However, they happen usually with brand new systems, straight out of the box and not older than 3 months or so.