Laptop CPU temperature steadily rises despite CPU usage never going over 20%?

XtremeAero426

Honorable
Jan 4, 2014
47
0
10,610
Laptop Specs:
Model: HP Elitebook 8470p
Processor: Intel i5 3340m
GPU: AMD Radeon HD 7570M 1GB GDDR5
RAM: 8GB SODIMM 1333MHz


My Laptop's CPU temperature starts at 35~36C and then steadily climbs up despite never going over 20% usage. It eventually settles around 65~70C but over time it'll slowly climb up to 95C where it shuts off despite usage still not changing. I've already tried replacing the thermal paste with the generic one that came with my Cooler Master CPU cooler but it has barely made a difference. I have also tried cleaning out the dust and nothing changed. What can I do to fix this?