The mode of heat transfer between earth and sun is -
radiation
Radiation is the process of heat transfer by electromagnetic waves or photons. It does not need a propagating medium. The energy transferred by radiation moves at the speed of light. The heat radiated by the sun can be exchanged between the solar surface and the earth's surface without heating the transitional space. There is no connecting medium between earth and sun. Therefore, radiation is the mode of heat transfer between sun and earth.