The current policy of managing high-level waste (HLW) derived in the closed nuclear fuel cycle consists in their vitrification into B-Si or Al-P vitreous forms. These compounds have rather limited capacity with respect to the HLW (5–20 wt%), and their properties change over time due to devitrification of the glasses. Cardinal improvement in the management of HLW can be achieved by their separation onto groups of elements with similar properties, followed by their immobilization in robust waste forms (matrices) and emplacement in deep disposal facilities. One of the possible fractions contains trivalent rare-earth elements (REEs) and minor actinides (MAs = Am and Cm). REEs are the fission products of actinides, which are mainly represented by stable isotopes of elements from La to Gd as well as Y. This group also contains small amounts of short-lived radionuclides with half-lives (T1/2) from 284 days (144Ce) to 90 years (151Sm), including 147Pm (T1/2 = 2.6 years), 154Eu (T1/2 = 8.8 years), and 155Eu (T1/2 = 5 years). However, the main long-term environmental hazard of the REE–MA fraction is associated with Am and Cm, with half-lives from 18 years (244Cm) to 8500 years (245Cm), and their daughter products: 237Np (T1/2 = 2.14 × 106 years), 239Pu (T1/2 = 2.41 × 104 years), 240Pu (T1/2 = 6537 years), and 242Pu (T1/2 = 3.76 × 105 years), which should be immobilized into a durable waste form that prevents their release into the environment. Due to the heat generated by decaying radionuclides, the temperature of matrices with an REE–MA fraction will be increased by hundreds of centigrade above ambient. This process can be utilized by selecting a vitreous waste form that will crystallize to form durable crystalline phases with long-lived radionuclides. We estimated the thermal effects in a potential REE–MA glass composite material based on the size of the block, the content of waste, the time of storage before immobilization and after disposal, and showed that it is possible to select the waste loading, size of blocks, and storage time so that the temperature of the matrix during the first decades will reach 500–700 °C, which corresponds to the optimal range of glass crystallization. As a result, a glass–ceramic composite will be produced that contains monazite ((REE,MA)PO4) in phosphate glasses; britholite (Cax(REE,MA)10-x(SiO4)6O2) or zirconolite ((Ca,REE,MA)(Zr,REE,MA)(Ti,Al,Fe)2O7), in silicate systems. This possibility is confirmed by experimental data on the crystallization of glasses with REEs and actinides (Pu, Am). The prospect for the disposal of glasses with the REE–MA fraction in deep boreholes is briefly considered.