Notebook Software and How To Questions

Hi I am not very good with the technical side of Laptops so just wanted to ask a question here.

I have a HP Pavilion g6 laptop (Intel Core i3 processer, 4 GB RAM) that I bought in mid December 2011 but have only just started to use. I set it up properly today, created my recovery discs and installed Norton anti virus.

I noticed that I can hear air/a fan blowing constantly while using the laptop. There is a vent on the left side of the laptop and if I put my hand in front of it I can feel coolish air blowing out. But the laptop feels warm-hot in a couple of areas, particularly to the left of the touch pad (bottom left of keyboard) and underneath I can feel the heat around about the center of the laptop.

So my question is, well two questions actually... should I be hearing a fan or air blowing constantly while the laptop is in use? It's just when I use my mothers Dell laptop I do not hear any air or fan blowing while in use. Also is it normal for the above two areas to be hot even though all I am doing is browsing the internet? Currently I have Internet Explorer open, Windows Live Messenger and that's it. I don't even have any files, photos or videos saved on the laptop yet as it is brand new. I previously owned a HP laptop about 3 years ago and it ended up shutting down by itself because it would get so hot. I am worried the same thing will happen and that I should have avoided HP because it's a common thing to happen with their laptops?