Na1/2Bi1/2TiO3 (NBT)-based materials are promising lead-free alternatives due to their large electrostrain and stable mechanical quality factor. Nonetheless, the relatively low depolarization temperature (Td) impairs its practical application. Recently, quenching from sintering temperature was adopted to increase Td of NBT-based ceramics. However, the origin of the quenching-induced increase in Td is still debated. In this study, quenching effects in (1-x)(0.4Na1/2Bi1/2TiO3-0.6BiFeO3)-xBaTiO3 ceramics are investigated. With increasing BaTiO3 content, this system transforms from ferroelectric to relaxor state at room temperature, with a criticality at x = 0.07, which exhibits R3c and P4bm coexisted phases. Ferroelectric and relaxor compositions exhibit different responses upon quenching. Upon quenching the ferroelectrics, Td increases from 420 to 580 °C for x = 0.04, but d33 is majorly unaltered. However, upon quenching the relaxors, Td increases marginally, while d33 increases from 62 to 97 pC/N. The correlation between the structural evolution and electrical responses upon quenching ferroelectric and relaxor compositions is explored.