temperature has an oscillating component, which is of great complexity. For a first estimate, we make two very simplifying assumptions: (i) We assume that the dipoles have a Debye dynamics with a given characteristic time τ ( T ). This is a simplifying assumption in the sense that when T is close to T$_{g}$ , it is well known that χ$_{1}$ ( ω ) is “stretched” with respect to a simple Debye law. In fact the Debye dynamics holds only at much higher temperatures, where the molecular motions are independent of each other, which allows to describe the non inertial rotational Brownian motion by the Smoluchowski equation for the probability distribution function of the orientations of the dipoles in configuration space [2, 7]. After an ensemble averaging of this equation, one gets the well known Debye equation for the dynamics of the average polarisation [2] : (ii) we assume that the main effect of δT$_{2}$ ( t ) is to modulate in time the value of τ while leaving unchanged the (Debye) dynamics. This can be justified by the fact that the temperature oscillation modulates the viscosity η , thus the relaxation time τ which is proportional to η . Considering the heatings of eq. (17), τ ( t ) is now given by where τ$_{lin}$ is the value of τ at zero field. In the following, δτ$_{2}$ will denote the amplitude of the 2 ω modulation of τ due to δT$_{2}$ ( t ) and corresponding to the last term of Eq. (19). Of course, using Eq. (19) for τ ( t ) assumes that δT$_{2}$ ( t ) instantaneously fully affects τ . A thorough modelization of this problem could lead to a more involved expression where δτ$_{2}$ should be weaker than in the above expression. As we shall find that the third harmonics is proportionnal to δτ$_{2}$/τ$_{lin}$ , see below Eq. (21), we are lead to the conclusion that our new estimate should, again, be slightly overstimated. We now insert τ ( t ) in Eq. (18) and set : where P$_{lin}$, Ψ$_{lin}$ , δP$_{1}$, Ψ$_{1}$ , P$_{3}$, Ψ$_{3}$ are to be determined. As we are only interested in the onset of nonlinear effects, P$_{lin}$ ∝ E is much larger than δP$_{1}$ ∝ E 3 and than P$_{3}$ ∝ E $^{3}$. This allows 20 P ( t ) = P$_{lin}$ cos( ωt − Ψ$_{lin}$) + δP$_{1}$ cos( ωt − Ψ$_{1}$) + P$_{3}$ cos(3 ωt − Ψ$_{3}$) + ... (20) τ ( t ) = τ$_{lin}$ + ( ∂τ$_{lin}$ ∂T ) δT$_{0}$ + ( ∂τ$_{lin}$ ∂T ) δT$_{2}$ ( t ) , (19) τ ∂P ∂t + P = ϵ$_{0}$ Δ χ$_{1}$E cos( ωt ) (18)