cpu core temperature
 

how can i be able to find the cpu core temperature using the cpu load and cpu usages.?
Is there any model to find the relation between core temperature and the cpu load?

You can't, the CPU needs to have a built-in thermometer (which all modern ones do).

actually i need to relate the cpu core temperature with cpu load.
how can i do so?

You simply can't.
The core temperature is dependent on more things than just CPU load. If you have a CPU with integrated memory controller (every AMD CPU since Athlon64/Opteron, every Intel Core i3/5/7 and Xeons based on this) then you have also to consider the work that the memory controller is doing, the same is true for integrated GPUs and things like PCIe-controllers.
You also have to think about the environments temperature, not only outside the case, but also inside. Working peripheral components, like harddisks, videocards and even parts of the mainboard will heat up underload, which causes the temperature in the case to rise. That will also cause higher CPU temperatures.

And also it depends heavily on the cooling system. Many even automatically adjust based on temperature.

Further to the above correct comments: When electronics guys try to work this out, they need exact ambient, watts used, and several specifications off various data sheets to approximate. Forget it.

From a scientist's perspective, what you are asking is whether anyone has yet built an "empirical" model of CPU temperature vs Load. For the isolated CPU case, I'm quite sure that the chip manufacturers have done something like this and you should refer to their data sheets or talk to their engineers. The problem is, as has been adequately pointed out above, that when a CPU is mounted on a mother board and put into a case, everything changes. However, there is nothing stopping you from doing this yourself if you want to go to the trouble of collecting and analyzing enough data. Most of the issues have already been pointed out. You would use the CPU core temperature that is reported using standard OS tools after applying various loads to the CPU. However, you need to repeat this experiment under a range of environmental conditions: Specifically temperature and humidity (which affects heat capacity of air). Each individual Machine would need to be characterized individually for reasons stated already by others. Finally, there is the issue of "kinetics" - that is, how long does the CPU, given its thermal environment and heat capacity, take to reach a steady state temperature at each CPU load.

Once you have spent several weeks collecting the data for one or two machines, you could indeed build a mathematical model that would reasonably well represent the Load vs. Temperature data with ambient environmental conditions as input parameters. Perhaps the bigger question is why? Simply watching core temperatures (either by eye, or with a software monitor, and then making suitable adjustments would probably be all that is needed in almost all cases - unless you are writing a scholarly paper on the subject. In any case, Have fun!