(A) Heater surface temperature:
The surface temperature of the heater is influenced by the amount of solar radiation received, but it does not directly affect the incident solar radiation.
(B) Day of the year:
The day of the year is important because solar radiation varies depending on the time of year due to the angle of incidence and the position of the Earth relative to the Sun.
(C) Hot water temperature:
The temperature of the hot water is influenced by the solar radiation absorbed, but it does not directly affect the incident solar radiation.
(D) Sky clearness:
The clearness of the sky directly influences the amount of solar radiation reaching the surface. Cloud cover can block or reduce the amount of solar radiation.
Final Answer:
\[
\boxed{\text{(B), (D)}}.
\]