We consider the Cauchy problem for the one-dimensional Timoshenko system coupled with the heat conduction, wherein the latter is described by the Gurtin-Pipkin thermal law. We study the decay properties of the system using the energy method in the Fourier space (to build an appropriate Lyapunov functional) accompanied with some integral estimates. We show that the number alpha(g) (depending on the parameters of the system) found in (Dell'Oro and Pata J Differ Equ 257(2): 523-548, 2014), which rules the evolution in bounded domains, also plays a role in an unbounded domain and controls the behavior of the solution. In fact, we prove that if alpha(g) = 0, then the L-2-norm of the solution decays with the rate (1 + t)(-1/12). The same decay rate has been obtained for alpha(g) not equal 0, but under some higher regularity assumption. This high regularity requirement is known as regularity loss, which means that in order to get the estimate for the H-s-norm of the solution, we need our initial data to be in the space Hs+s0, s(0) > 1.