Context. X-ray cavities and extended radio sources ("cocoons") surrounding active galactic nuclei (AGN) have been detected by the Chandra X-ray mission and radio interferometers. A joint analysis of X-ray and radio maps suggests that pressure values of non-thermal radio-emitting particles derived from the radio maps are not sufficient to inflate the X-ray cavities. We propose using the Sunyaev-Zel'dovich (SZ) effect, whose intensity strongly depends on the pressure, to find the hitherto undetected, dynamically-dominant component in the radio cocoons. Aims. Numerical simulations show that plasma with a high temperature (10(9)-10(10) K) is a good candidate for inflating the AGN cocoons. To constrain the population of high energy electrons inside AGN cocoons that is predicted by numerical simulations, we study different methods for maximizing the contribution of such energetic electrons to the SZ effect. Methods. Our calculations of intensity maps of the SZ effect include relativistic corrections and utilize both analytic models and numerical 2D simulations. Results. We demonstrate that the spectral function at a frequency of 217 GHz has an absolute maximum at a temperature higher than 10(9) K, therefore the measurement of the SZ effect at this frequency is a powerful tool for potentially revealing the dynamically-dominant component inside AGN jet-driven radio cocoons. A new method is proposed for excluding the contribution from the low energy, non-relativistic electrons to the SZ effect by means of observations at two frequencies. We show how one may correct for a possible contribution from the kinematic SZ effect. The intensity maps of the SZ effect are calculated for the self-similar Sedov solution, and application of a predicted ring-like structure on the SZ map at a frequency of 217 GHz is proposed to determine the energy released during the active jet stage. The SZ intensity map for an AGN cocoon in a distant elliptical is calculated using a 2D numerical simulation and including relativistic corrections to the SZ effect. We show the intensity spectrum of the SZ effect is flat at high frequencies if gas temperature is as high as k(b)T(e) = 500 keV.