τ$_{c}$/τ$_{e}$ is similar to that presented in Ref. [13]: where γ is the degeneracy factor, 〈 E$_{Z}$ 〉 = E T $_{Z}$+ E C Z 2 is the average value of the two Zeeman splittings of the channel and of the trap respectively, δ = ∣ E T Z − E C Z ∣ and Δ$_{ST}$ is the en- ergy gap between the singlet and the triplet energy levels in the doubly occupied defect. The generalized temperature for such system extracted from the fitting is T$_{fit}$ = 0 . 80(1) K. Δ$_{ST}$ =150(5) µ eV is due to the different charging energy caused by the different orbital symmetry of the electron wavefunction for the singlet and the triplet states. The differ- ence between the generalized electron temperature and the lattice temperature which is in thermal equilibrium with the $^{3}$He at 310 mK is consistent with other reported values in similar systems. To conclude, we experimentally determined the generalized temperature of a system of few electrons at cryogenic temperature. We have shown that below 10 K the capture and the emission of a point defect may be thermally activated and we discussed the role of phonons. We realized such mesoscopic system in a n-MOSFET, where a point defect exchanges one electron with the 2DES at the Si/SiO$_{2}$ interface. The generalized tem- perature is extracted from the probability of occupation of a mesoscopic system constituted by a point defect capable of containing either 1 or 2 electrons in thermal contact with a dilute electron system, in the limit of finite N , with the help of a static magnetic field. This method provides an estimate of the temperature of a system consisting of a localized electron in thermal exchange with a small number of electrons confined in two dimensions. 5 [1] H. Sellier et al., Phys. Rev. Lett. 97 , 206805 (2006) [2] G. P. Lansbergen et al., Nature Physics, doi:10.1038/nphys994 (2008) [3] E. Prati et al., Phys. Rev. B80, 165331 (2009) [4] F. Giazotto et al., Rev. Mod. Phys. 78, 217 (2006) [5] E. Prati et al., J. Appl. Phys., 103, 123707 (2008) [6] M.Sanquer et al., Phys. Rev. B. 61 , 7249 (2000) [7] L. Landau, L. Lifshitz, Statistical Physics (Course of Theoretical Physics, Volume 5) 3ed., Pergamon (1980) τ$_{c}$ τ$_{e}$ = γe β ( E T +Δ 12 $_{−}$µ ( N ) ( 1+ 3 2 N $^{))}$( cosh β 〈 E$_{Z}$ 〉 + cosh β δ $_{2}$) 1 + e $_{−}$β Δ ST (1 + 2 cosh βE T $_{Z}$) (2)