We have studied the effect of hypothetical Cosmions on the core stability of main sequence stars (of populations I and II). Cosmions, with a mass of 4-10 Gev/c2 and a scattering cross section with nucleons of approximately 10-36 cm2 could prevail in transporting heat in the stellar cores. Raby [17] showed the existence of a local thermal instability caused by the presence of Cosmions in the solar core. Here we have used more accurate analytic relations and have considered all of the main sequence stars which have captured an efficient number of these hypothetical particles from their birth up to the present time. We have found a wide range of probable instabilities in the stellar cores for various values of Knudsen number, cosmion mass and cosmion cross section.