We consider the theory of thermoelastic phase transformations with an additive Gibbs potential for the case when the dissipation rate is proportional to the square of the rate of variation of a parameter determining the phase content. Using this approach, we obtain the relation between graphs of differential scanning calorimetry and a diagram of the phase transfer in the case of no stresses. We propose a piecewise-quadratic approximation of diagrams of the phase transfer corresponding to piecewise-linear approximation of graphs of differential scanning calorimetry. We obtain numerical solutions for couple problems on direct transformation for a rod made from an alloy with shape memory. We state that there presence essential difference between the distribution of temperature and the distribution of a parameter of phase content over a material and variation of these parameters in time obtained by using linear and piecewise-quadratic approximations for diagrams of transfer.