The speed-gradient variational principle (SG-principle) is formulated and applied to thermodynamical systems. It is shown that Ziegler's Maximum Entropy Generation Principle as well as Prigogine's principle of minimum entropy production and Onsager's symmetry relations can be interpreted in terms of the SG-principle. For an SG thermodynamic system its negative entropy plays a role of the goal functional. The speed-gradient formulation of thermodynamic principles provides their extended versions, describing transient dynamics of nonstationary systems far from equilibrium. As an example an SG-model of transient(relaxation) dynamics for systems of a finite number of particles based on maximum entropy principle is derived. It has the form dN(t)/dt = AlnN(t), where N(t) is the vector of the cell populations, A is a symmetric matrix with two zero eigenvalues corresponding to mass and energy conservation laws.