Quantum reactive and elastic cross sections and rate coefficients have been calculated for D(+) + H2 (v = 0, j = 0) collisions in the energy range from 10(-8) K (deep ultracold regime), where only one partial wave is open, to 150 K (Langevin regime) where many of them contribute. In systems involving ions, the ∼R(-4) behavior extends the interaction up to extremely long distances, requiring a special treatment. To this purpose, we have used a modified version of the hyperspherical quantum reactive scattering method, which allows the propagations up to distances of 10(5) a0 needed to converge the elastic cross sections. Interpolation procedures are also proposed which may reduce the cost of exact dynamical calculations at such low energies. Calculations have been carried out on the PES by Velilla et al. [J. Chem. Phys. 129, 084307 (2008)] which accurately reproduces the long range interactions. Results on its prequel, the PES by Aguado et al. [J. Chem. Phys. 112, 1240 (2000)], are also shown in order to emphasize the significance of the inclusion of the long range interactions. The calculated reaction rate coefficient changes less than one order of magnitude in a collision energy range of ten orders of magnitude, and it is found in very good agreement with the available experimental data in the region where they exist (10-100 K). State-to-state reaction probabilities are also provided which show that for each partial wave, the distribution of HD final states remains essentially constant below 1 K.