This paper reports results from a study of the reaction pp → pK0Σ+ at beam momenta of p beam = 2950, 3059, and 3200 MeV/c (excess energies of ε = 126, 161, and 206 MeV. Total cross-sections were determined for all energies; a set of differential cross-sections (Dalitz plots; invariant-mass spectra of all two-body subsystems; angular distributions of all final-state particles; distributions in helicity and Jackson frames) are presented for ε = 161 MeV. The total cross-sections are proportional to the volume of available three-body phase space indicating that the transition matrix element does not change significantly in this range of excess energies. It is concluded from the differential data that the reaction proceeds dominantly via the N(1710)P 11- and/or N(1720)P 13-resonance(s); N(1650)S 11 and Δ(1600)P 33 could also contribute.