The authors are experts in the field of elasto-plasticity, and published several articles on related topics, such as the Prandtl-Reuss flow law in plasticity. Here they consider thermoplastic materials with a linear evolution of kinematic hardening. Their mathematical model is a modification of the Prandtl-Reuss model for elastoplasticity with the yield function dependent on the temperature. The admissible stresses vanish as the material reaches critical temperature. Basically the state of the material is determined by the displacement vector \(u\), the stress tensor \(T\) and the temperature \(\theta\). Actually \(\theta\) is the difference between temperature of the material and the reference temperature \(\theta^*\). The state of an elastic material is described by the following system of partial differential equations: \[ \begin{aligned} \text{div\,}T(x, t)&= -F(x,t)\text{ (equilibrium), }T(x,t)={\mathcal D}(1/2(\nabla u(x,t)+\nabla^T u(x,t)))\\ \theta_t(x, t)&= \kappa\Delta\theta(x, t)- \gamma\text{\,div\,}u_t(x,t)\text{ (heat transfer)}.\end{aligned} \] Here \({\mathcal D}\) is the constant, positive definite and symmetric elasticity tensor. Analogously the constitutive (matrix) equation of thermo-plasticity is given by: \[ T(x,t)={\mathcal D}(\varepsilon(x, t)- \varepsilon^p(x, t))- c\theta(x, t)I=- F(x,t). \] Here \(I\) denotes the identity matrix. The authors assume the Prandtl-Reuss flow rule, with strain tensor \(\varepsilon^p(x,t)\) evolving with time. Such system is analyzed, and it works well if thermal effects are ignored. For details of such analysis the readers are referred to the article of \textit{R. Temam} [Arch. Ration. Mech. Anal. 95, 137--183 (1986; Zbl 0615.73035)]. The authors admit that the presence of thermal effects makes analysis very complicated. The approximate model proposed by Yosida allows the authors to prove convergence of stresses and strains of the \(L^2\) solutions of such slightly modified thermo-plastic system.