Modern processors are often tested to the speed they need to run at, and graded based on that - so your processor probably has spent a fair bit of time at your maximum suggested clockspeed.
In addition, one of the legacies of the notoriously hot pentium IV family is that most modern processors come with a thermal cutoff - so its very likely that with the modern core2 or corei5/7 based systems its more likely that your system will shut down if it overheats, than literally burn out. Toms hardware had a video where they removed a heatsink from a PIV and an old K7, and well, that's a unlikely situation - and the PIV merely stuttered, and modern AMDs have far better thermal protection than the K7
So, no. It's unlikely to burn anything out with a heatsink and no overclocking.