Abstract <p>In this work we study a two-dimensional problem in magneto-thermoelasticity for a half-space model. An internal heat source of constant magnitude is acting in the half-space. This study sought to improve the comprehension of wave propagation in magneto-thermoelastic materials according to Classical theory of elasticity (CT) by developing precise wave solutions for the governing equations that take into consideration temperature-dependent material features. The analytical expressions of displacement components, stress components and temperature field are obtained by Lame’s potential method and normal mode analysis technique. The numerical values of these functions are represented graphically. The work includes detailed graphical representations of crucial discoveries such as temperature distributions, stress components, and displacement components which provide amazing visual insights into the complex interactions that occur within thermo-elastic systems. From the distributions, it can be found the wave type heat propagation in the medium. A comparison is made with the results obtained in the presence and absence of the magnetic field.</p>