Frequency shift of hyperfine transitions due to blackbody radiation

We have performed calculations of the size of the frequency shift induced by a static electric field on the clock transition frequencies of the hyperfine splitting in Yb+, Rb, Cs, Ba+, and Hg+. The calculations are used to find the frequency shifts due to blackbody radiation which are needed for accurate frequency measurements and improvements of the limits on variation of the fine-structure constant alpha. Our result for Cs [delta nu/E-2=-2.26(2)x10(-10)Hz/(V/m)(2)] is in good agreement with early measurements and ab initio calculations. We present arguments against recent claims that the actual value might be smaller. The difference (similar to 10%) is due to the contribution of the continuum spectrum in the sum over intermediate states.