In the quest of YBa2Cu3O7-δ (Y123) bulk superconductors providing strong magnetic fields without failure, it is of paramount importance to achieve high thermal stabilities to safeguard the magnetic energy inside them during the trapping-field process, and sufficient mechanical reliability to withstand the stresses derived from the Lorenz force. Herein, we experimentally demonstrate a temperature rise induced by dissipative flux motion inside an Y123 thin-wall superconductor, and a significant thermal exchange in a composite bulk Y123 cryomagnet realized by embedding this superconductor with high thermal-conductivity metal network. It resulted in stimulating the maximum trapped field Bm, which reached 6.46 T on 15.9 mm-diameter single disk superconductor after magnetization by field cooling to 17 K under 7 T, leading to an improvement of 18% compared to the thin-wall superconductor. The composite cryomagnet particularly revealed the potential to trap stronger fields if larger magnetic activation is available. By virtue of the pore-free and crack-free microstructure of this cryomagnet, its strength σR was estimated to be 363 MPa, the largest one obtained so far for Y123 bulk superconductors, thus suggesting a striking mechanical reliability that seems to be sufficient to sustain stresses derived from trapped fields stronger than any values hitherto reported.