When the definition of the unit of time and time scales with atomic clocks was introduced in 1967 the shift of the atomic reference frequency from the interaction with blackbody radiation was not considered. In 1982, Itano, Lewis and Wineland published the first calculation of the effect  with the result that at 300 K temperature the relative frequency shift for a caesium clock would be -1.7E-14, due predominantly to a differential quadratic Stark shift of the hyperfine levels of the s-ground-state. The size of the effect was slightly bigger than the systematic uncertainty of the most precise caesium clocks at that time. Since these devices had not been designed to accomodate significant temperature changes, an experimental verification of the effect remained a challenge for some time. The first quantitative study was reported by Bauch and Schröder at PTB in 1997  with a dedicated setup where the caesium atoms passed through tubes that could be heated to 480 K. Also in 1997, the SI definition of the second was amended with the clarification "the definition refers to a caesium atom at rest at a temperature of 0 K". This emphasizes the requirement to correct for the effects of the relativistic Doppler shift (time dilation) and the presence of thermal radiation. In modern atomic clocks with laser cooled atoms the Doppler shifts are usually small and well controlled, but when the apparatus is operated at room temperature the effects of BBR may make a dominant contribution to the systemativc uncertainty budget.
In optical atomic clocks  which reach relative uncertainty in the E-18 range the effect of BBR can be controlled by selecting a reference transition with small differential polarizability due to the intrinsic atomic structure, and by placing the atom in a homogeneous environment of well controlled temperature (cryogenic or close to room temperature) and applying a correction based on the accurately known differential polarizability, or by a combination of the above methods.
 W. M. Itano, L. L. Lewis, D. J. Wineland, Phys. Rev. A 25, 1233 (1982)
 A. Bauch, R. Schröder, Phys. Rev. Lett. 78, 622 (1997)
 A. D. Ludlow, M. M. Boyd, Jun Ye, E. Peik, P. O. Schmidt, Rev. Mod. Phys. 87, 637 (2015)