Magnetic field and temperature dependence of the properties of the ground state of the strong-coupling bound magnetopolaron in quantum rods (QRs) with hydrogenic impurity is studied by means of the Huybrechts-Lee-Low-Pines transformation method and the quantum statistical theory. The expressions for the ground-state energy and the mean number of phonons of the magnetopolaron are derived. Results of the numerical calculations show that the bound state of the magnetopolaron cannot be formed when the value of the aspect ratio of the QR, the dielectric constant ratio, the electron-phonon coupling strength or the temperature parameter is small. The larger the deviation of the value of aspect ratio e' from 1 is, the more it is unfavorable to the stability of the ground state of the magnetopolaron. When the magnetopolaron is in the bound state, the absolute value of its ground-state energy and its mean number of phonons increase with an increase of the dielectric constant ratio and confinement strength of QRs, but decrease with an increase in the cyclotron frequency of the external magnetic field and the temperature. The absolute value of the ground-state energy and the mean number of phonons of the magnetopolaron decrease with decreasing e' when e'<1, but decrease with increasing e' when e'>1. They get the maximum value at e'=1.