If the sun is not hot enough how it performs fusion?

Our star Sun is really hot, we are talking about some serious temperature's here. The temperature of it's core is about 15 million degree Celsius but the problem comes here,  theoretically for fusion to occur we need temperature of about 100 million degree Celsius ,so how come our sun perform fusion !HOW! . Now without wasting any time let's dig for the real answer. 

             

For fusion to occur protons need to be push so hard against the  Electromagnetic repulsion between them that they pass the  coloumb barrier after which Strong force takes the control and they fuse. But our sun is not hot enough to do this (remember temperature is a measure of kinetic energy) ,  but its temperature is enough to push and bring the protons close to the coloumb barrier , and here the magic happens. And to get it we need to get a little "Quantum" here the phenomenon of quantum tunneling takes control ,and another thing to consider is that in a given temperature particles always exist in a variety of energy some with high and some with comparatively low so some come very close to the coloumb barrier and some can't. 

           

 The phenomenon of Quantum tunneling to be really simple is that a subatomic particle can (or there is a very low probability that it will ) tunnel through a barrier to the other side, which seems impossible,  but its 'quantum mechanics' anything can happen here.Now let's get to the point and you'll see that everything just connects.

       

   Among the highly energetic protons inside the sun which come very close to the coloumb barrier, sometimes due to quantum tunneling it tunnels or pass the coloumb barrier and "Bamm" they fuse! But one thing to know is that ,this happens really I mean really Rarely .  Now you might think ,then how our sun produce so much energy per second. The answer is simple its damm big and the protons are really small, so even if the chances of it happening is less, that less is actually really big.