The temperature dependences of the derived exact values of the life times of the metastable states described by some piece-wise linear and piece-wise parabolic potential profiles are investigated. The shape of the potential barrier along with the shape of the other potential profile parts is shown to effect essentially on the metastable state life time τ and on its temperature dependence at any values of the potential barrier height Е. It is demonstrated that well-known Arrhenius low τ = θ0ехр(Е/КТ) (θ0 = const) is correct only for some particular shapes of the potential profile and under small mtensity of fluctuations КТ << Е. It is shown that various deviations of the temperature dependence of the metastable state life times from е Arrhenius low when the prefactor θ0, becomes а function of the temperature, may be explained by the taking into account both the nonparabolic shapes of potential barrier and well and the arbitrary choice of the potential barrier height E in comparison with the fluctuation intensity KT. The various dependences of θ0(KТ) caused by the different specific shapes of the potential wells and barriers under kT << E are given at the end of this paper.