This work reports on theoretical investigation of the temperature and hydrostatic pressure effects on the confined donor impurity in a AlGaAs-GaAs hollow cylindrical core-shell quantum dot. The charges are assumed to be completely confined to the interior of the shell with approximately rigid walls. Within the framework of the effective-mass approximation and by using a variational approach, we have computed the donor binding energies as a function of the shell size in order to study the behavior of the electron-impurity attraction for a very small thickness under the influence of both temperature and hydrostatic pressure. Our results show that the temperature and hydrostatic pressure have a significant influence on the impurity binding energy for large shell quantum dots. It will be shown that the binding energy is more pronounced with increasing pressure and decreasing temperature for any impurity position and quantum dot size. The photoionization cross section is also analyzed by considering only the in-plane incident radiation polarization. Its behavior is investigated as a function of photon energy for different values of pressure and temperature. The opposite effects caused by temperature and hydrostatic pressure reveal a big practical interest and offer an alternative way to tuning of correlated electron-impurity transitions in optoelectronic devices. (C) 2018 Elsevier B.V. All rights reserved.