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There exists strong geomorphological, sedimentary and mineralogical evidence that Mars had an active surface hydrological cycle during the Noachian period, about 3.8 Gyr ago (Ga). However, how surface temperatures compatible with perennial liquid water could be sustained in spite of a Sun that only had 75% of its present-day brightness has remained elusive, leading to the faint young Sun paradox for Mars. Recently, the greenhouse effect of hydrogen peroxide (H 2 O 2 ) has been proposed as a solution by Ito et al. (2020). Radiative transfer models have shown that a few ppmv of H 2 O 2 in a 1 or 2 bar CO 2 atmosphere could solve the faint young Sun paradox on early Mars. In a warm and wet CO 2 atmosphere, H 2 O 2 is produced by photochemistry and contributes to the stability of the CO 2 atmosphere along with the HO x (H, OH and HO 2 ) catalytic cycles. Nevertheless, a thorough assessment of the viability of such a high H 2 O 2 abundance is still lacking. Using 1D and 3D climate models coupled with a C-H-O photochemistry solver, we show that in the most favourable case for H 2 O 2 to build up, its steady-state abundance is several orders of magnitude short from its required abundance of ∼ 1 ppmv to have a significant radiative effect. Furthermore, we also show that a transient warming episode associated with massive H 2 O 2 release cannot exceed 10 Martian years. We therefore rule out H 2 O 2 as a warming agent for early Mars. • An upper bound for the abundance of hydrogen peroxide (H 2 O 2 ) in a warm and wet early Mars atmosphere is determined using coupled 3D global circulation model and photochemistry simulations. • Hydrogen peroxide does not exceed a few ppbv in a 2 bar CO 2 atmosphere, which is too low to induce greenhouse warming. • In a warm and wet early Mars atmosphere, CO 2 restoration relies approximately as much on odd hydrogen (H, OH and HO2)-based as on hydrogen peroxide-based catalytic cycles. • Transient extreme release of hydrogen peroxyde dissolved in an ice cap might raise the surface temperature above 273 K for less than 10 Martian years at most.