The thermal stability of the dielectric behavior and the crystal structure, surface morphology, polarization, and piezoelectric properties of lead-free BiGaO3 (BG)-modified 0.65Bi(1.0)5FeO(3)-0.35BaTiO(3) (abbreviated as BF-BT-xBG with 0 <= x <= 0.03) ceramics were investigated. XRD analysis of BF-BT-xBG dielectric ceramics revealed no remarkable change in the crystal structure within the studied composition range. Around the critical composition (BF-BT-0.02BG), the piezoelectric constant (d(33)) and electromechanical coupling factor (k(p)) reached maximum values of similar to 205 pC/N and 34.5%, respectively. The BF-BT-BG dielectric system also exhibited a thermally-stable epsilon(r) (801-902, at 30 degrees C 500 degrees C), high T-max (395 degrees C 416 degrees C), colossal epsilon(rmax) (46,363-76,303), and epsilon(rmid) (2241 +/- 15%-3678 +/- 15%, with tan delta <= 0.08) across a wide temperature range of 198 degrees C-332 degrees C. This improvement in the dielectric properties and high T-max of the optimum specimen can be attributed to the BiGaO3-modification and quenching process, which made the system viable for applications that require high-temperature dielectric stability.