Technically, it’s not cooling, but transferring heat to a heat pipe or heat sink 
Most probably there should be a video of someone disassembling your laptop model (or some similar one), use some search engine. Start with grounding yourself (touch something metal, not small), unplug power supply and battery.
I’m using isopropyl alcohol to soften and clean old thermal paste with a paper towel and cotton swab. Rice grain sized compound should be enough for a processor in 10 years old laptop. Just be gentle, the chip probably won’t have any metal heat spreader, so don’t damage it.
2 Likes