This paper is concerned with investigating the asymptotic behavior of end effects for a generalized heat conduction problem with an added dissipation term defined on a three-dimensional semi-infinite cylinder. With homogeneous Dirichlet conditions on the lateral surface of the cylinder it is shown that solutions either grow exponentially or decay exponentially in the distance from the finite end of the cylinder. In particular, to render decay estimate explicit, we pattern after the analysis of Payne and Song [13, 15]. The continuous dependence effect of perturbing the equations parameters is also investigated.