That would depend on your definition of damage.
First of all your equipment is going to 'wear down' much faster if the CPU is at 100% load longer than an hour or so. Normal computer usage lets the CPU throttle somewhere between 20% load and 100% for let's say 6 to 8 hours a day. CPU coolers are made to prevent the CPU from overheating in all possible situations, so it won't burn out your CPU immediately.
But with normal computer usage your CPU will heat up, cool down a bit (a bit less hot), heat up again, etc. With mining on a CPU, the CPU will heat up and continue heating up to the point where the heat exchanged by the CPU cooler will be equal to the heat produced by the CPU. This is called an equilibrium (or balance).
There are temperatures your PC would be OK with running 24/7, but that does not mean anyone would recommend you doing so. You won't ruin your computer right away, but the chances of it will definitely be higher.
Next to that, the amount of bitcoins you can generate letting your CPU mine bitcoin right now (December 2014) would be around 0.00000001 a week... ? That's about accurate. (Not taking power usage into account.) If you really want to mine cryptocoins on your CPU, look for a CPU-only cryptocoin and then exchange the mined coins to Bitcoin, that way you'll get much more in most cases.
If you absolutely want to mine Bitcoin directly without mining an altcoin, look at this: How do I start mining?
