In the paper, the influence of stain and heat effect caused by the variation of stresses in the temperature governing equation, and the influence of temperature variation in the constitutive equations and the non-Fourier effect of heat conduction are all considered, and the thermo-mechanical equation of isotropy and linear thermo-elastic material including the temperature gradient is deduced. The influence of relax time on the space-time distributions of temperature increment and stresses are discussed in the ceramic membranes with finite thickness for 1-D transient question which subjects to single pulse heat deposition. The result shows that, for the ceramic, the difference of speed between heat wave and expand wave reaches the order of magnitude, and the couple effect of thermo-mechanics has little influence on the speed of propagation. Since the single pulse heat deposition belongs to the thermal physical quantities, the heat wave is the domain speed of propagation, and the mechanical quantities belong to the high-order small quantities.