A coarse-grained bead spring model of short polymer chains is studied by constant pressure molecular dynamics (MD) simulations. Due to two competing length scales for the length of effective bonds and the energetically preferred distance between nonbonded beads, one observes a glass transition when dense melts are cooled down (as shown in previous work, at a pressure p=1 the mode coupling critical temperature is at T(c)approximate to0.45 and the Vogel-Fulcher temperature is T(0)approximate to0.33, in Lennard-Jones units). The present work extends these studies, estimating a cooling-rate-dependent glass transition temperature T-g(Gamma) by cooling the model system from T=0.6 down to T=0.3, applying cooling rates from Gammaapproximate to10(-3) to Gammaapproximate to10(-6) (in MD time units), and attempting to identify T-g(Gamma) from a kink in the volume versus temperature or potential energy versus temperature curves. It is found that T-g(Gamma) lies in the range 0.43less than or equal toT(g)(Gamma)less than or equal to0.47, for the cooling rates quoted, and the variation of T-g(Gamma) for Gamma is compatible with the expected logarithmic variations. We will show why a detailed distinction between competing theories on these cooling rate effects would need an excessive amount of computer time. To estimate also the melting transition temperature T-m of this model, the sytem was prepared in a crystalline configuration as an initial state and heated up. The onset of diffusion, accompanied by an isotropization of the pressure tensor was observed for T(m)approximate to0.77. This implies that the model is suitable for studying deeply supercooled melts.