Blackbody radiation is expected to produce a temperature-dependent Stark shift in atomic Rydberg states. Unfortunately; in "one-electron" atoms; all the Rydberg levels experience the same shift; and the effect is only observable on an optical transition from the ground state. However; in a many-electron atom the presence of valence-state perturbers leads to unequal shifts of the Rydberg levels. This should make it possible to observe the frequency shift of a transition between two neighboring Rydberg states at a frequency in the radio-frequency range. This eliminates the need for a very stable visible laser; which so far has been the major technical obstacle to the observation and utilization of the effect. We present as an example a specific case in Ba.