connected to the cell through a thermal impedance. This device allowed a temperature regulation with a precision of ∼ 50 mK, and a temperature quench from 300 to 200 K in ∼ 1.5 hour. The electrodes of the two capacitors are 6 mm thick rods of high purity copper on which 200 nm of gold was evaporated to prevent the formation of any oxydized layer. A highly specialised surface treatment reduced any surface defects: The final roughness was about 10 nm, while the planeity, i.e. the difference between the highest point of the electrodes and the mean plane, was better than 1 µ m. Most of the results presented in the letter were obtained with Mylar R ○ spacers depicted in the letter, giving inter-electrode distances of 19 µ m and 41 µ m for the two samples. For completeness, we have added a few results obtained very recently by using spacers made of resin patterned by photolithography (with a thickness L = 12 µ m for the thin sample and 25 µ m for the thick sample). The bridge was fed by a low distortion voltage source (Stanford Research Systems R ○ DS360) which gave a rms excitation voltage ≤ 14V at a frequency f = ω/ 2 π ranging from 10 mHz to 200 kHz. The nonlinear susceptibility χ$_{3}$ was determined after having carefully checked the cubic dependence of the measured signal at 3 ω with respect to the excitation at 1 ω . Last, for a significant fraction of the frequencies and temperatures investigated here, we have checked the quantitative consistency between the 3 ω signal measured in our “two sample bridge” and the one found with the “twin T notch filter” depicted in Ref. [1], which allows to measure χ$_{3}$ by a different method. Let us consider a sample made of a supercooled liquid excited by an oscillating field E cos( ωt ). For small enough E values, the resulting polarisation P$_{lin}$ is linear and reads : When E is increased, a part of the nonlinear response comes from the dissipated electrical power, the volumic density of which is p ( t ) = 1 $_{2}$ϵ$_{0}$ χ ′′ $_{1}$ωE$^{2}$(1 + cos(2 ωt − φ )), with φ = − π + 2 arctan( χ ′′ $_{1}$/χ ′ $_{1}$) (see e.g. Appendix of Ref. [3]). The resulting heat propagates towards a IV) HEATING EFFECTS CALCULATIONS P$_{lin}$ ( t ) ϵ$_{0}$E = χ ′ $_{1}$cos( ωt ) + χ ′′ 1 sin( ωt ) . (11) 17