  The subject of this paper is to study the decay of solutions for two systems
of laminated Timoshenko beams with interfacial slip in the whole space R
subject to a thermal effect of type III acting only on one component. When the
thermal effect is acting via the second or third component of the laminated
Timoshenko beam (rotation angle displacement or dynamic of the slip), we prove
that both systems are polynomially stable and obtain stability estimates in the
L2 -norm of solutions and their higher order derivatives with respect of the
space variable. The decay rates, as well as the absence and presence of the
regularity-loss type property, depend on the regularity of the initial data and
the speeds of wave propagations. However, when the thermal effect is acting via
the first comoponent (transversal displacement), we introduce a new stability
number \c{hi} and prove that the stability of systems is equivalent to \c{hi}
6= 0. An application to a case of lower order coupling terms will be also
given. To prove our results, we use the energy method in Fourier space combined
with well chosen weight functions to build appropriate Lyapunov functionals.
