The dynamics of a series of entangled cis-1,4-polyisoprenes located within self-ordered nanoporous alumina templates are studied as a function of the degree of confinement, 2R(g)/d (R-g is the radius of gyration and d is the pore diameter) with dielectric spectroscopy and temperature-modulated differential scanning calorimetry. For the higher molecular weights, the segmental dynamics obtained on cooling speed-up under confinement resulting in a lower glass temperature, T-g, with respect to the bulk, scaling as Delta T-g = -62 X (2R(g)/d). This effect is discussed in terms of the proposed relation of the glass temperature to the interfacial energy. Under confinement, a new process appears with an Arrhenius temperature dependence and with a dielectric strength that increases linearly with the increasing degree of confinement. This mode is discussed in terms of the adsorption/desorption kinetics of segments in the vicinity of the pore walls. The particular geometry employed here with the electric field being parallel to the polymer/surface interface maximizes the contribution of adsorbed segments. Moreover, with temperature-modulated differential scanning calorimetry and dielectric spectroscopy, we address the origin of the dual glass temperature, T-g, found on the heating traces. By employing several temperature/annealing protocols, we show that the higher T-g is conditional; it appears only when the lower T-g is crossed on the previous cooling run. These findings could suggest that the lower T-g is the one closer to equilibrium.