I bought a thinkpad T420 last month and have the random freeze problem on windows 7 64 bit like many of your computer. I had tried a lot of ways but failed to solve it.
a few days before I was trying to test the system's thermal capability with a tool. It takes about 30% of CPU on backend. The testing lasted for 24 hours, the machine was still running! the CPU temp is about 72C. The machine freezed after 1 or 2 hours after the test program closed.
After that I always keep a testing program running on backend. It takes about 15%-20% of the CPU, the machine haven't freezed for a few days!!! That is really crazy but it works!
best way to stop random freezes and system hangs on a new laptop is to uninstall all the OEM branded software that is pre installed with the laptop or just to fresh install windows onto the laptop for best results. also dont use avast its a system hog and causes all sorts of problems.