I'm reading up on star formation and from what i've understood so far, is that protogalactic clouds with density fluctuations cool and then fragment after which, they fragment again into subfragments. Now do the density in these individual subfragments increase the temperature enough to start nuclear fusion? and what is the temperature in which fusion can start? I know that an increase in temperature alone isn't enough to start fusion. So what does happen to make the temperature increase besides the density and collapsing of the cloud?