Elastic properties of mixtures of illitic clay, thermal power plant fly ash (fluidized fly ash—FFA and pulverized fly ash—PFA), and grog were investigated during the heating and cooling stages of the firing. The grog part in the mixtures was replaced with 10, 20, 30, and 40 mass% of the fly ash, respectively. The temperature dependence of Young’s modulus was derived using the dynamical thermomechanical analysis, in which dimensions and mass determined from thermogravimeric and thermodilatometric results were used. Flexural strength was measured at the room temperature using the three-point bending test. The following results were obtained: (1) Bulk density showed a decreasing trend up to 900 °C and a steep increase above 900 °C. During cooling, the bulk density slightly increased down to the room temperature. (2) Young’s modulus increased significantly during heating up to ~300 °C. Dehydroxylation was almost not reflected in Young’s modulus. At temperatures higher than 800 °C, Young’s modulus began to increase due to sintering. (3) During cooling, down to the glass transformation, Young’s modulus slightly increased and then began to slightly decrease due to microcracking between phases with different thermal expansion coefficients. (4) Around the β→α quartz transition, radial stresses on the quartz grain altered from compressive to tensile, creating microcracks. Below 560 °C, the radial stress remained tensile, and consequently, the microcracking around the quartz grains and a decreasing Young’s modulus continued. (5) With a lower amount of PFA and FFA, a higher Young’s modulus was reached after sintering. The final values of Young’s modulus, measured after firing, show a decreasing trend and depend linearly on the part of fly ash. (6) The flexural strength measured after firing decreased linearly with the amount of the fly ash for both mixtures.