well, cpus do get hot while working, and generally get hotter by the amount of work they do. more work they do, more and more parts of their silicon are active contributing to the total power consumption and thereby heat generation of the cpu.
as for proportions, there is no fixed relationship, and it varies by cpus, type of job they are doing, and the length of time they are doing that job. generally heavy duty processing (like playing a 3D game like Quake3, or rendering a complex image or doing some long complex math) the cpus heat up fast. i think its because it is now when the special purpose sections of cpu do the work alongwith the standard sections that always work while you do your routine work. and working hard makes them add to the heat generation.
<font color=blue>die-hard fans don't have heat-sinks!</font color=blue>
Yep, as you give the processor more work to do, more transistors have to switch. That's current flowing to more transisitors, and more heat dissipated. Probably around 2x, but i'm no electrical engineer.
The bottom line is that your temperature will increase during high loads, unless you are cooling the wholey-liquid-nitrogen out of the processor.
No, heat generation is usually expressed in watts. For example, my space heater puts out 12,000 watts. If you desribe heat generation as a temperature rise of an object, then the mass of the object must be known.
It's all in how you look at it. You can tell someone how much power (heat) an object is putting out, but give the wrong impression. If the surface area is great enough, you can put out (transfer) 1500W with only a 1C temp. difference. Or you can have a blow torch putting out well in excess of 3000W, with a surface area of a few square centimeters. They are both very physical functions, usually called 'state' functions. Temperature tells you how much (average) energy is contained in the material, contributing to the vibration of the atoms.
Thermodynamics all relates back to the production of beer. Everything hinges on how much beer you can produce.