The capability of optical reference cavities to resist ambient thermal fluctuations is significant in ultrastable laser systems especially applying in transportable system and space station. To reduce the deterioration of long-term laser frequency stability induced by temperature variation, the thermal response of cavities is investigated. The simulation and analysis indicate that the use of multiple enclosing thermal shields with a low emissivity allows a larger thermal time constant. The quantitative functional relationships between the thermal time constant and the heat capacity and surface emissivity of the passive thermal shields are firstly obtained using FEA simulation. Based on these results, a temperature-insensitive cavity system is designed with a thermal time constant of approximately 680 h. According to the designed system, two different methods are used to evaluate the thermal performance. And mathematical expressions for the cavity temperature over time are obtained. The calculated thermal time constant is validated by the simulated results. The thermal sensitivity of the designed system is 4.1 x 10(-11) and 1.3 x 10(-5) when temperature variation period is 1 h and 24 h, respectively. The fractional length instability of the cavities induced by temperature fluctuation is 8.2 x 10(-16) over an average time of 1 day, which can compete theoretically with fountain clocks.