We investigate how the shear and the temperature quadrupole anisotropy of the radiation during the early epoch of the universe may contribute to the evolution of the Bianchi type I universe. To connect bolometric multipoles and the temperature anisotropy, we suggest a simple form of an anisotropic distribution function. We find evolution equations for the shear, the monopole, and the quadrupole temperatures. Furthermore, we analyze their dynamical behavior during the radiation-dominated era and interpret the quadrupole temperature as the shear viscosity of radiation. With a numerical implementation, we discuss how they evolve as the universe expands until the monopole temperature arrives at the current monopole value of the cosmic microwave background temperature power spectrum. It is shown that the initial values of the shear and the quadrupole temperature of radiation can affect the current observational values, even when the shear component is only dominant in the very early regime of the universe. To be explicit, we have found that the temperature anisotropy due to the quadrupole could compose almost up to 20% of the total temperature, provided that the current proportion is approximately 0.001%.