Part of the solar energy gain is not radiated into space, it maintains a 15 million degrees hot plasma in the Sun's interior.
Hydrogen becomes fully ionized, the protons may fuse. The fusion reactor "Sun" may operate in a permanent regime since gravitational forces keep its fuel trapped.
The high density of matter, strong electromagnetic fields, and the size of this reactor above all, make the merger of four protons sufficiently probable for maintainance of the fusion 'fire'.
To be sure, however, the process is more complicated than the quadruple collision shown here, it proceeds in three steps - and takes millions of years to complete\!