A widely adopted approach to form matched seals in metals having high coefficient of thermal expansion (CTE), e.g. stainless steel, is the use of high CTE glass-ceramics. With the nucleation and growth of Cristobalite as the main high-expansion crystalline phase, the CTE of recrystallizable lithium silicate Li2O-SiO2-Al2O3-K2O-B2O3-P2O5-ZnO glass-ceramic can approach 18 ppm/degrees C, matching closely to the 18 ppm/degrees C-20 ppm/degrees C CTE of 304L stainless steel. However, a large volume change induced by the - inversion between the low- and high- Cristobalite, a 1(st) order displacive phase transition, results in a nonlinear step-like change in the thermal strain of glass-ceramics. The sudden change in the thermal strain causes a substantial transient mismatch between the glass-ceramic and stainless steel. In this study, we developed new thermal profiles based on the SiO2 phase diagram to crystallize both Quartz and Cristobalite as high expansion crystalline phases in the glass-ceramics. A key step in the thermal profile is the rapid cooling of glass-ceramic from the peak sealing temperature to suppress crystallization of Cristobalite. The rapid cooling of the glass-ceramic to an initial lower hold temperature is conducive to Quartz crystallization. After Quartz formation, a subsequent crystallization of Cristobalite is performed at a higher hold temperature. Quantitative X-ray diffraction analysis of a series of quenched glass-ceramic samples clearly revealed the sequence of crystallization in the new thermal profile. The coexistence of two significantly reduced volume changes, one at similar to 220 degrees C from Cristobalite inversion and the other at similar to psi 470 degrees C from Quartz inversion, greatly improves the linearity of the thermal strains of the glass-ceramics, and is expected to improve the thermal strain match between glass-ceramics and stainless steel over the sealing cycle.