This is a loaded question. What is "normal?"
For almost any well designed and ventilated system running "normal" applications (email, web browser, Word processor), the stock heat sink and fan will work fine.
If you keep your system in a sealed box, desk drawer or closet with no air flow. no heat sink / fan is going to keep it cool.
If you run 100% processor intensive applications (some games, CAD and video editors) things could get warm.
The best bet if you are concerned is to down load a tool like CPUID HWmonitor http://www.cpuid.com/softwares/hwmonitor.html and keep an eye on the CPU core temp.
If you find that your usage seems to run up into the 80's, I would think about getting a better cooling solution.
Thanks for the timely and helpful reply, Doc_SilverCreek.
I'll download the tool you suggested and monitor the temps. For starters I'll be operating in the "normal" range with a well ventilated box. I'm going to build a new system using either an i3 or an i5 processor and plan to do some video editing, no gaming, and mostly other "normal" computer activities.
My question also was trying to verify that the BX at the start of the Intel part number does indeed mean that a heat sink/fan is included with the processor. That used to be the case when I was buying Pentium and Celeron processors. This will be my first Core i5 purchase. No where in the Intel literature do they clarify that the heat sink/fan in included in the BX part. Looks like it is.
The cooling solution on i3 / i5 is perfect for them, even with slight OC it would do very nice. Some of the high-end super-duper coolers are even worst then the stock ones so even that say enough for the quality and engineering gone in the design of the cooling solution for the i-core's. I for one was pleasantly surprised with the cooling on the i-cores, because there was some problems with stock coolers with some dual's.
If you go for non-stock cooling solutions better go with something that is more expensive, but tried and tested with good results under heavy load ( i guess if you going to change cooler it would be because the use of some intensive applications or games ) there are quite a big bunch of reviews and tests in the net and almost all include the stock cooling so you can check them out.
The FHS that comes with your boxed processor has the same warranty as your processor... three years.
I would use the FHS that ships with your processor and be conifident you have a three year warranty when using it.
There is a lots of Engineering that goes into a FHS used on Intel processors... believe it or not.