Athlon 64 processors are designed to be used in desktops where they get better airflow, but many notebook manufacturers will use them (and P4s) regardless. It could be that it's getting slightly warmer than you noticed before because the thermal paste between the core and heatsink is thinning out and not conducting heat onto the heatsink as well as before. Even a slight increase in temps can trigger the BIOS to shutdown the system before damage to a component occurs.

Do you notice is shuts down quicker when you've been using processor-intensive applications? Like running a virus or spyware scan?

You can always enter your machine's BIOS by hitting a key while the machine is booting up. It should tell you what that key is. Try F2, Delete or F12 if you can't. The notebook's user manual should say. Once in the BIOS there should be a section that shows your cpu and motherboard temps. The cpu should idle somewhere around 40-65C. Anything in the 70's and definitely anything in the 80's is bad.