deduced from low bias current and presumably limited by contact barriers. As seen in the figure, a full shot noise limit is observed for | V$_{d}$ | ≲ 0 . 4 V, followed by a saturation plateau. Although the noise characterization is certainly relevant for understanding the saturation mechanism that takes place in nanotubes at very high bias, we prefer to leave this discussion for a future work. Using S$_{I}$ = 2 eI$_{d}$ ˜ F ≳ 4 g DC d k$_{B}$T$_{e}$ ( g$_{m}$ ≃ 0 and g$_{d}$ ≳ g DC d in Eq.(1)) we deduce ˜ F ≳ 2 k$_{B}$T$_{e}$/eV$_{d}$ and an (over-) estimate of electronic temperature k$_{B}$T$_{e}$/eV$_{d}$ ≲ ˜ F/ 2 ≃ 0 . 6. Indeed, this ratio is larger than a theoretical expectation, k$_{B}$T$_{e}$/eV$_{d}$ ∼ √ 6 D/π 2 ∼ 0 . 25, for a Wiedemann-Franz resistance limited thermal sink [14]. Importantly, both numbers show that a hot electron regime is expected and present in the nanotube. As discussed below, we can rely on the transconductance characteristics for an independent determination of the electronic temperature of the nanotube working as a transistor. Fig.4 contains the main experimental results of the paper, namely the bias dependence of I$_{d}$ , S$_{I}$ and g$_{m}$ , at the transconductance maximum ( V$_{g}$ = +0 . 5 V). The S$_{I}$ ( V$_{d}$ ) dependence is similar to that observed in the open state with, as a difference, a first noise plateau ( ˜ F ≃ 0 . 7) observed in range | V$_{d}$ | = 0 . 1–0 . 3 V. The two step increase of noise and the width of the plateau ( ∼ 0 . 3 V) are suggestive of the subband structure of the nanotube (intersubband- gap ∼ 0 . 3–0 . 5 eV for a 2 nm diameter). In order to secure 1D transport conditions, we shall therefore focus below to the ( | V$_{d}$ | ≲ 0 . 3 V) bias range. For the theoretical analysis we rely on a simple 1D nano-transistor model. The nanotube is described as a fourfold degenerate 1D channel decomposed in three sections (see Fig.1(c)): a central part covered by the top-gate which acts as a local classical barrier and two ungated nanotube leads on both sides which constitute the drain and source reservoirs of the tran- sistor. The leads are diffusive and assumed to be populated with Fermi distributions f$_{s}$ ( E ) and f$_{d}$ ( E ) = f$_{s}$ ( E + eV$_{d}$ ). The barrier (height Φ) acts as an high-pass energy filter with quasi-ballistic high energy electrons (transmission D ( E ) ≲ 1 for E > Φ) and reflected low energy ones ( D ( E ) = 0 for E < Φ). With these assumptions and scattering theory [13] one can readily calculate current and noise to deduce the differential conductance g$_{d}$ = 4 e 2 h f$_{d}$ (Φ), the transconductance g$_{m}$ = β 4 e 2 h [ f$_{s}$ (Φ) − f$_{d}$ (Φ)] , (2) and the noise conductance g$_{n}$ = 2 e 2 h [ f$_{s}$ (Φ) + f$_{d}$ (Φ)]. According to the equivalent circuit in Fig.1(b), we have taken ∂ Φ /∂V$_{g}$ = − eβ . These three ”conductances” depend on two parameters, the drain and source occupation numbers (at E = Φ), and therefore obey the 4