In L₂(R^d; Cⁿ) , we consider a semigroup e-tAε, t⩾ 0 , generated by a matrix elliptic second-order differential operator A_ε⩾ 0. Coefficients of A_ε are periodic, depend on x/ ε, and oscillate rapidly as ε→ 0. Approximations for e-tAε were obtained by Suslina (Funktsional Analiz i ego Prilozhen 38(4):86–90, 2004) and Suslina (Math Model Nat Phenom 5(4):390–447, 2010) via the spectral method and by Zhikov and Pastukhova (Russ J Math Phys 13(2):224–237, 2006) via the shift method. In the present note, we give another short proof based on the contour integral representation for the semigroup and approximations for the resolvent with two-parametric error estimates obtained by Suslina (2015).