The simple cubic spin-1 Ising model exhibits the ferromagnetic (F)-ferromagnetic (F) phase transition in the low temperature region for the interval 1.40 < d = D/J < 1.48 at k = K/J = -0.5. The degree of the F-F phase transition determines the special point on the (k(B)T/J, d) phase diagram. In this paper, the critical behavior of the F-F phase transition was investigated for different heating rates using the cellular automaton heating algorithm. The universality class and the type of F-F phase transition were analyzed using the finite-size scaling theory and the power law relations. The results show that the F-F phase transition may be the second order, the first order or the weak first order depending on the heating rate in the interval 1.40 < d < 1.48 for k = -0.5.