Why is my notebook very warm?
Because the machine is using processors that are using electrons and switches to calculate things it's working on.
These electrons are passing through extremely tiny connections at the speed of light and encountering slight imperfections in the material and also other nuclear forces known as resistance.
When resistance occurs, it generates heat.
The heat is transmitted to internal cooling system that draws in outside air and fan(s) blows it over it and out the rear of the machine. Thus transferring that heat to the local environment.
Therefore it's important to follow certain procedures to keep your machine from overheating.
1: Do not block the vents around the machine or the keyboard.
2: Do not place it on a bed or other material that will hold in heat, like your lap. Rather place on stiff board or desk and slightly elevate the back of the machine so even more air gets underneath as the bottom also acts like a heat distributor.
3: Have your machine periodically (annually or more) cleaned of internal dust by Apple.
4: Avoid dusty, floating hair and fiber areas as that gets inhaled into the machine and clogs the cooling fins behind the fans.
5: Certain machines like the 13" MacBook Pro and under lack a separate dedicated graphics processor, thus the main processor is also doing the graphics, which place two sources of heat on the same location, making for a much warmer machine than people expect. The 15" MacBook Pro has a separate graphics processor, thus is a much cooler machine, provided it's function is enabled to be used all the time (Energy Saver > graphics switching off), not just when more graphics performance is needed.
6: Use the machine in a below 80º F air conditioned clean room type environment.
7: Quit any and all open programs your not currently using, because if you have them running, it's taking up memory and if you go over your RAM, then it's using the storage drive as extra memory and that can cause more heat.
8: Your machine has automatic procedures in place to reduce heat if the cooling system is overloaded, this may result in sluggishness in using the machine. If this occurs then backup your files off the machine and take it in for service.
9: If you hear anything like clicking, buzzing, scrapping, etc., it might be a warped spindle on your fans which then rub the fan housing. Have it replaced.
10: Install third party fan and cooling monitoring software like Hardware Monitor.
10.8+ users hold control key and click on program, choose "Open" to bypass OS X Gatekeeper controls as this program can't do it's required function due to AppStore restrictions, thus not on there.
http://www.bresink.com/osx/HardwareMonitor.html
11: Compare your observations with other stats here. Mind that one starts from a cold boot and test, not a already overheated machine which might take a long time to cool down first.