The method of orthogonal projection is applied in the first stage of thermoelastic problems involving specification of the temperature field in a uniform, infinitely long, elastic bar heated by an electric current, the surface of the bar being kept at zero temperature. Three kinds of cross sections of the bar are considered: elliptical, equilateral triangular, and in the form of a circular sector. All the function-space concepts that are used are briefly explained, but the treatment is purely intuitive.