POLARBEAR-2 (PB-2) is a cosmic microwave background (CMB) polarization experiment for B-mode detection. The PB-2 receiver has a large focal plane and aperture that consists of 7588 transition edge sensor (TES) bolometers at 250 mK. The receiver consists of the optical cryostat housing reimaging lenses and infrared filters, and the detector cryostat housing TES bolometers. The large focal plane places substantial requirements on the thermal design of the optical elements at the 4K, 50K, and 300K stages. Infrared filters and lenses inside the optical cryostat are made of alumina for this purpose. We measure basic properties of alumina, such as the index of refraction, loss tangent and thermal conductivity. All results meet our requirements. We also optically characterize filters and lenses made of alumina. Finally, we perform a cooling test of the entire optical cryostat. All measured temperature values satisfy our requirements. In particular, the temperature rise between the center and edge of the alumina infrared filter at 50 K is only 2:0 ± 1:4 K. Based on the measurements, we estimate the incident power to each thermal stage.