Yes, you will notice that a constant running fan in a desktop with a Pentium 4 will be even more pronounced and consistent in a notebook with a Pentium 4M as there is less space for fan cooling in a notebook.
Therefore, the Pentium M (Centrino) is the best choice for a true notebook user right now (especially for lighter weight and thinner cases and longer battery life -- 3.5 to 5 hours as opposed to 2 hours average or even less in some cases for a Pentium 4M).
The HPZT3000/Compaq X1000 sisters I have are a good place to start if you want a 15.4" widescreen (6.5 pounds) and up to 64mb of dedicated video RAM (see X1000forums.com and Hpshopping.com)
The HPDV1000 is an example of a 14" widescreen Pentium M with shared video only (not video card for dedicated video) at 5.3 pounds. See DV1000forums.com
Also, Dell has the 8600 15.4" widescreen at 6.9 pounds with a dedicated video card (ATI 9600) or the Dell 600M in a smaller LCD Pentium M notebook.
Check these out but there are other Pentium M (Centrino) models like Gateway at Best buy and Toshiba (although some Toshibas lately have been having static issues).
A key selling point of my HPZT3000/Compaq X1000 model is that the fan does not come on at all in normal use except at startup and when you are either using the optical drive heavily (playing a DVD or CD or loading software) or when the hard drive is working hard. it is completely silent when surfing the web (on wi-fi for me) and I use it in front of my TV.
Some other notebooks can run a bit hotter even with the Pentium M processor (especially the Toshibas) so be aware to try out the specific model if you want the fan not to be running alot.
But the key is to avoid the hot running Pentium 4M altoghether. The Athlon 64 is better but still runs more hot at this point (low voltage cpu coming out).
I am going to buy a notebook. My priority is that the machine does not get very hot, so the fan does not need to work very often, and that the fan be the silence as possible.
I will be greatefully if you give me some advise about this.
(I will need a PC no a Mac, since I have to test games with it).