Calculate the average temperature needed for hydrogen fusion reaction my question is simple. How can we calculate the temperature needed in order to do the nuclear fusion things , and also the temperature after the reaction successful.

If you can describe it, it would be really cool. I just want to know about it
Thanks
 A: Firstly, fusion doesn't happen in the way depicted in the question.  Four protons don't participate in a 4-body reaction.  Instead there are many intermediate steps:
![enter image description here][1]
Each step has its own reaction rate.  The overall reaction rate is determined by the [rate limiting step][2].  The proton-proton reaction is the rate limiting step in this case.
It is important to think in terms of the rate at which a reaction occurs, rather than whether or not it will occur.
The reaction rate will depend on temperature and pressure.  In the Sun, pressure is ~265 billon bar, so the reaction can proceed at 10-15 million K.  The rate of reaction is actually very low, the center of the Sun only produces energy at rate of ~277 Watts per cubic meter.  On Earth, we can not built a reactor with pressure this high, so higher temperature is needed.  Different reactions such as starting with deuterium or tritium are used to avoid the need for the proton-proton reaction.  Then fusion could be achieved in the ~100 million K range for example.
Of note, the first step in the reaction is only possible because of the weak force, in which one of the protons spontaneously changes into a neutron. This is an extremely unlikely occurrence, and is in fact the primary reason the sun lasts for billions of years
[1]:https://upload.wikimedia.org/wikipedia/commons/thumb/7/78/FusionintheSun.svg/421px-FusionintheSun.svg.png
[2]: http://en.wikipedia.org/wiki/Rate-determining_step
