Kenneth...be sure to use some new heatsink grease between the CPU and the heatsink. The gray stuff on that laptop is likely old and crunchy. Scrape it all away with a plastic tool and clean with alcohol first....both the heatsink and CPU.
The other reasons for random shutdowns on that model....bad batteries in combination with a wonky power connector or charger cord. Also re-seat the memory modules.
The D620 is a workhorse. It's got a magnesium frame, WAY more solid than the junk you see in retail models today. You can find CPU upgrades on ebay for under $20, I think the D620 handles 4GB of RAM, and swap out the spinner for an SSD.....like a new system, almost. ;-)