It is possible that the motherboard is reporting the temp wrong, although that means it usually would have always been reporting the wrong temp. The 'sensor' for the processor temperature is on-die inside the CPU. Its highly unlikely that its 'bad' itself, but the data its sending may be misinterpreted. Sometimes a new BIOS will update the temperature reading algorithm.
What is the motherboard reporting for ambient temperature?
Is the air in the case (or exhausting out the back) warm/hot? Does the heatsink feel particularly hot? Have you been overclocking this CPU/RAM/GPU?
Going from 50c to 60/65c (idle to heavy load) isn't necessarliy out of the ordinary. The lockups are the bigger issue. Those will be a symptom of some other root cause. Running 65-70c probably isn't that root cause. I'd kick the tires on the rest of the system a little bit. Memtest... especially with the system 'heated up'. Extra heat in the system could be causing other components (memory or GPU) to slide out of their comfort zones leading to the instability. I'd also download a program like
HWMonitor to monitor the GPU temps. I have friends who's GPUs overheating caused lockups.