In this paper we present radiative‐convective simulations to test the idea that tropical cirrus clouds, acting as a negative feedback on climate, can provide a solution to the faint young Sun paradox. We find that global mean surface temperatures above freezing can indeed be found for luminosities larger than about 0.8 (corresponding to ∼2.9 Ga and nearly complete tropical cirrus coverage). For luminosities smaller than 0.8, even though global mean surface temperatures are below freezing, tropical mean temperatures are still above freezing, indicating the possibility of a partially ice‐free Earth for the Early Archean. We discuss possible mechanisms for the functioning of this negative feedback. While it is feasible for tropical cirrus to completely eliminate the paradox, it is similarly possible for tropical cirrus to reduce the amounts of other greenhouse gases needed for solving the paradox and therefore easing the constraints on CO2 and CH4 that appear to be in disagreement with geological evidence.