The recently found superconductor MgCNi3 is investigated by specific heat measurements. Strong electron-phonon coupling is derived from the superconducting part. An unusual magnetic field dependent low temperature upturn of the specific heat is analyzed in terms of ferromagnetic spin fluctuations, suggesting suppression of superconductivity from Tc ≈ 20 K to Tc ≈ 7 K. The results are discussed within a proposed two-band model, also explaining so far not fully understood transport measurements.