The relationship between clock speed and heat output

I been thinking and could it be ture that when you increase the clock speed that the heat generate becomes much than the increase in speed, I try explain what I mean with the following for example:
Say if you had a 3ghz cpu at default voltage cpu and it generated 90watts of heat, then would the same cpu at 6ghz default voltage would generate 360watts of heat.
I know that that high speed and voltage is not possible, its only intented to give you an idea of what im trying to say.

You are thinking about a very reasonable mathematical relationship.

Essentially what you are asking/proposing is that the relationship between FSB (in effect, clock speed) and heat output may not be a 1 to 1 (1:1) relationship.

Example: If you simplify the relations between clockspeed and wattage they are easier to compare. I will use the numbers you proposed:

3Ghz/6Ghz = 1/2; 90watts/360watts = 1/4;

With a 1:1 relationship between clockspeed setting and resultant wattage then both fractions would equal 1/2 - double clockspeed, double heat output. Your example however, has double the clockspeed and quadruple the wattage - a 1:4 relationship.
End example

The relationship between FSB and heat output behaves as somewhat of a direct relationship - as you increase FSB a little, heat output will increase a little. I think people call the relationship between FSB and heat output a 1:1 relationship.

The relationship between a voltage increase and heat output on the other hand could not be considered 1 to 1. A very slight increase in voltage will mean a considerably larger increase in heat output.

Ive always wondered what sort of relationship speed and thermal dissipation had, for the most part i dont think that it is a linear relationship, i.e. a linear function x^1, i always thought that it was more of a 10^X type of relationship, also dont forget that the thermal dissipation differs when process size is changed, so its sort of like a stepped function. Grrr, hard to explain. Ill try plugging in some numbers to may calc and fit a curve.
xb-70