The purpose of our research is to investigate a thermoelastic
Timoshenko system with an infinite memory term on the shear force
while the bending moment is under the influence of a thermoelastic
dissipation. We prove that the system`s stability holds for a
broader class of relaxation functions. Under this class of
relaxation functions $h$ at infinity, we establish a relation
between the decay rate of the solution and the growth of $h$ at
infinity. Moreover, we drop the boundedness assumptions on the
history data. We employ Neumann-Dirichlet-Neumann boundary
conditions for our result. In comparison to the bulk of results in
the literature, which frequently enforce the equal-wave-speed
constraint, this result is of tremendous importance because our
result does not require any conditions on the parameters.