We present the results of three-dimensional simulations of the deep convective envelope of a young (10 Myr) 1 M☉ star, obtained with the anelastic spherical harmonic code. Since young stars are known to be faster rotators than their main-sequence counterparts, we have systematically studied the impact of the stellar rotation speed, by considering stars spinning up to 5 times as fast as the Sun. The aim of these nonlinear models is to understand the complex interactions between convection and rotation. We discuss the influence of the turbulence level and of the rotation rate on the intensity and the topology of the mean flows. For all of the computed models, we find a solar-type superficial differential rotation, with an equatorial acceleration, and meridional circulation that exhibits a multicellular structure. Even if the differential rotation contrast ΔΩ decreases only marginally for high rotation rates, the meridional circulation intensity clearly weakens according to our simulations. We have also shown that, for Taylor numbers above a certain threshold (Ta ≳ 109), the convection can develop a vacillating behavior. Since simulations with high turbulence levels and rotation rates exhibit strongly cylindrical internal rotation profiles, we have considered the influence of baroclinic effects at the base of the convective envelope of these young Suns to see whether such effects can modify the otherwise near-cylindrical profiles to produce more conical, solarlike profiles.