The sun transfers thermal energy to the earth by what energy

-- Thermal energy can move from one place to another by
conduction, convection, or radiation. 

-- Conduction and convection need a material substance to
move through.  Radiation doesn't. 

-- Since there's no material substance between the Sun and
the Earth, that right there tells us that the heat and light we get
from the sun all gets here by the process of radiation.