(see [14]). The resulting temperature increase is the sum of a constant term and a term δT$_{2}$$_{ω}$ ( t ), oscillating at 2 ω . This δT$_{2}$$_{ω}$ ( t ) oscillation leads to a modulation of the linear sus- ceptibility δχ$_{1}$ ( ω )( t ) = ( ∂χ$_{1}$ ( ω ) /∂T ) δT$_{2}$$_{ω}$ ( t ), thus to a 3 ω modulation of the polarization P ( t ) ∝ χ$_{1}$E . We calculated precisely this 3 ω heating contribution using the heat propaga- tion equation [14]. This calculation gives an upper limit to the heating effects contribution, in particular for f ≥ f$_{α}$ , because the finite relaxation time τ of the molecules prevents them from following instantaneously the temperature oscillation δT$_{2}$$_{ω}$ ( t ) (as already advocated by Richert et al. [24]). A representative example of these calculations is given on Fig. 4 : the heating effects are negligible in most of the frequency range of interest, in particular around the χ$_{3}$ ( ω ) peak. Thus, our estimate of N$_{corr}$ ( T ) and the power-law dependence of χ$_{3}$ ( ω ) are not affected by heating. Our results should allow significant progress of models which predict or assume dynamical correlations in supercooled liquids. Such models should not only reproduce the increase of the correlated volume we found as T → T$_{g}$ (see Fig. 3), but they should also account for the magnitude and shape of χ$_{3}$ ( ω, T ), given by the H function in Eq. (1), which carries an important information on the physics of the dynamical correlations [12, 13]. Recently, Richert et al. put forward a phenomenological model [21, 24, 25] which accounts for their nonlinear susceptibility data at 1 ω . In this model, the supercooled liquid is thought of as a collection of “Debye-like” dynamical heterogeneities ( dh ), each of them having its own relaxation time τ$_{dh}$ . The model posits that the electrical power absorbed by each dh raises its temperature above that of the phonon bath. A non-trivial and crucial assumption is that heat exchange between the slow degrees of freedom and the phonon bath is set by the local relaxation time τ$_{dh}$ , and not by a microscopic vibration time. As a result, each dh has its own fictive temperature with a dc and an ac component. Again, the ac component δT$_{dh,}$$_{2}$$_{ω}$ ( t ) leads to a 3 ω “heating” contribution to the polarization P ( t ). Such a contribution to χ$_{3}$ should however not be considered to be in competition with the critical dynamical correlations related to the glassy dynamics [12, 13]. As this model assumes a priori the existence of dynamical heterogeneities, it should be seen as a phenomenological description of the influence of dynamical correlations on the nonlinear susceptibility. We calculated the prediction of this model for the 3 ω nonlinear response and found that χ$_{3}$ ( ω ) is indeed peaked at a frequency of the order of 1 /τ ( T ). However, some assumptions are needed to generalize the model to the 3 ω response. These assumptions influence the magnitude and 9