I know of no way to test a CPU out of a system or without a special purpose test rig of some sort.
CPU's don't operate in full performance modes until everything is initialized and the OS starts to load up. I don't even think all 8 cores are enabled in BIOS as they're not needed. Although, CPU power saving features are also not enabled, that's why they can get pretty warm just in BIOS on only one core. But the CPU may never have gotten hot enough and even if it did protections might just shut it down before it got to the point of damaging it. So, you may be correct and the problem really is that your system simply can't handle a 3700X....either that or properly clamping on the heatsink will cool it correctly and allow it to work. But B350's never were intended to run 2nd gen and it's a bit dodgy trying to run one on them even when it works right.
Assuming this is what you mean, it's perfectly safe sitting in the clam shell package it came in. It's designed to protect the delicate pins as well as against electro-static discharges.