I"d just electrical tape it to the fan on the heatsink. Sticking it under the heatsink is too close IMO, but I doubt it would cause any issues.
Of course, to reiterate, do NOT put it in between the CPU and the heatsink. Only thermal paste should go there.
No its not check out my pic, been running a digital display for 2 years with it near the core, wont harm if the tip is touching a little its on the top than squeezing the heat sink down where the problem is but its your decision I would not dare give someone advice that would kill their cpu.
I think I would trust the motherboard sensors more, but its always nice to have a backup temperature sensor. But to each their own. I wouldn't do it myself, but that doesn't mean its bad to do it.