Skhandelwal, the problem with the elementary physics concepts such as energy, force, etc. are that they are usually
harder to understand than derived concepts (mass, movement, etc) because it is these concepts that we observe in nature, and fundamental concepts are often either abstract or not defined (they are simply there, as a starting point for our physical description).
It is possible for energy to turn into mass. This is exactly what the famous (and often mis-quoted) formula E = M c^2 (or \gamma m c^2) says: energy and mass can be converted into each other. This is also what we observe in nuclear reactions where particles split or fuse, where the new (sum of) mass(es) is smaller than the original (sum of) mass(es), the remaining mass having been converted to energy. In fact, energy and mass are completely equivalent in principle (though in practice it's everything but easy to convert between them). As to why part of the energy of the universe is ... well, energy (light, heat, radio waves, etc) and some of it is in the form of mass, and why that part is what it is, I don't really know, so I'm afraid I also cannot give you the reason that energy started to be converted to mass when the temperature cooled. (Actually, I'm making here a distinction I just said doesn't really exist... so probably I'm making a conceptual mistake here.)
As for temperature, we should first look at entropy. Entropy tells us something about the number of states accessible to a system (actually, if there are
g states in which a quantum system may be, the entropy is \sigma = \log g). Nature always seeks to increase entropy (simple example: a solid may evaporate, because then all the particles in the solid are free to move about in a gas, which gives each particle more degrees of freedom - hence more entropy). Now temperature, basically, measures how much a system wants to exchange entropy with another system. Suppose we have one (closed) system divided into two subsystems. It may be possible that one subsystem sacrifices some entropy, so that the entropy of the other system increases - in such a way that the
overall entropy increases. Actually, if the systems are left free to do what they want, they will do this until there is an equilibrium (thermal equilibrium): both systems have maximal entropy. In this case, the temperature is defined to be equal in both the systems. The more "drive" there is to exchange entropy, the higher the temperature will be.
That is the way I like to look at it, for other points of view and a more precise treatment you should take a look at
this page or a good book (like the one from Kittel and Kroemer).