“thermostat” which in our case can be considered to be the copper electrodes (thickness 6 mm, diameter 20 mm). The resulting average sample temperature increase δT ( t ) is where the mean dc temperature increase δT$_{0}$ is larger or equal than the ac one δT$_{2}$ , thus at any time δT ( t ) ≥ 0. φ$_{2}$ is a phase shift related to heat transport. As our measurements give the nonlinear dielectric response averaged over the sample volume, δT ( t ) in equation (12) is the temperature increase averaged over the same volume. Using equations (11)-(12), we thus obtain for the nonlinear part of the susceptibility due to heating effects: This is an upper limit on the contribution of heating to the nonlinear response, since we have assumed that δT ( t ) induces instantaneously a modification of the susceptibility. As already advocated in Ref. [3], this is questionable, specially in what concerns the contribution of δT$_{2}$ ( t ) which should be averaged out because of the finite relaxation time τ of the system (see after eq. 17). By using equations (12-13), one gets : The four terms in the right hand side of equation (14) give the nonlinear response of the system due to heating that we define in general by In the right hand side of equation (15) each of the four terms are proportional to E $^{2}$. χ ′ 3 ,h and χ ′′ 3 ,h do not depend on E , while ( δχ ′ $_{1}$)$_{h}$ and ( δχ ′′ $_{1}$)$_{h}$ are proportional to E $^{2}$. Our notations 18 P ( t ) − P$_{lin}$ ( t ) ϵ$_{0}$E = ( δχ ′ $_{1}$)$_{h}$ cos( ωt ) + ( δχ ′′ $_{1}$)$_{h}$ sin( ωt ) + E 2 4 χ ′ 3 $_{,h}$cos(3 ωt ) + E 2 4 χ ′′ 3 $_{,h}$sin(3 ωt ) . (15) P ( t ) − P$_{lin}$ ( t ) ϵ$_{0}$E = [( δT$_{0}$ + 1 2 δT$_{2}$ cos( φ$_{2}$ ) ) ∂χ ′ 1 ∂T + 1 2 δT$_{2}$ sin( φ$_{2}$ ) ∂χ ′′ 1 ∂T ] cos( ωt ) + [( δT$_{0}$ − 1 2 δT$_{2}$ cos( φ$_{2}$ ) ) ∂χ ′′ 1 ∂T + 1 2 δT$_{2}$ sin( φ$_{2}$ ) ∂χ ′ 1 ∂T ] sin( ωt ) + [ 1 2 δT$_{2}$ cos( φ$_{2}$ ) ∂χ ′ 1 ∂T − 1 2 δT$_{2}$ sin( φ$_{2}$ ) ∂χ ′′ 1 ∂T ] cos(3 ωt ) + [ 1 2 δT$_{2}$ sin( φ$_{2}$ ) ∂χ ′ 1 ∂T + 1 2 δT$_{2}$ cos( φ$_{2}$ ) ∂χ ′′ 1 ∂T ] sin(3 ωt ) . (14) P ( t ) − P$_{lin}$ ( t ) ϵ$_{0}$E = ( ∂χ ′ 1 ∂T δT ( t ) ) cos( ωt ) + ( ∂χ ′′ 1 ∂T δT ( t ) ) sin( ωt ) . (13) δT ( t ) = δT$_{0}$ + δT$_{2}$ cos(2 ωt − φ$_{2}$ ) , (12)