The paper discusses the possibility of active control of flow and heat transfer using a magnetic field and suction in a generalized form. The unsteady temperature two-dimensional laminar magnetohydrodynamic boundary layer of incompressible fluid on a porous body of arbitrary shape is analyzed. Outer electric filed is neglected, magnetic Reynolds number is significantly lower than one i. e. the considered problem is in inductionless approximation. Characteristic properties of fluid are constant and it is assumed that a uniform suction or injection of a fluid, same as the fluid in primary flow, can take place through the body surface. The boundary-layer equations are generalized such that the equations and the boundary conditions are independent of the particular conditions of the problem, and this form is considered as universal. Obtained universal equations are numerically solved using the “progonka” method. Numerical results for the dimensionless velocity, temperature, shear stress and heat transfer as functions of introduced sets of parameters are obtained, displayed graphically and used to carry out general conclusions about the development of temperature magnetohydrodynamic boundary layer. [Projekat Ministartsva nauke Republike Srbije, br. TR 35016]