the problem with the sun that size isnt that something cant heat the earth from that distance,
i posted this in another thread
unless the sun is really dense, it doesnt seem the right size to fit how much H2 He, and Li it has. And if it is that dense, it would have burned out a long time ago. if it isnt that dense, then the fusion reactions would occur too infrequently for it to give off much heat at all (and probably never have Li inside it at all).
Basically, the sun is nearly the heat it needs to do the fusion reactions, so it does it by the ever elusive quantum tunneling. The amount of particles is sufficient to keep this going at a healthy rate (it wont burn out in 2 seconds, burn us, or keep us cold). However, a denser sun would be hotter