Utilizing polarization maintaining photonic crystal fiber (PM-PCF) with the low temperature coefficient of birefringence, a two-dimensional tunable and temperature-insensitive Lyot filter aiming to compensate the frequency modulation to amplitude modulation (FM-to-AM) conversion in high power laser facility is demonstrated. The Jones matrix is applied to analyze the relationship between optical characteristics of the filter and physical parameters (including amplitude ratio, phase delay, and susceptibility of the birefringence to temperature) of the polarization optical field. Both the transmission peak wavelength and extinction ratio of the spectral transmission are able to be changed simultaneously, hence, it shows more efficient FM-to-AM compensation ability. Besides, the transmission peak shift is about 18 pm/℃ with the PM-PCF configuration, which is about two orders of magnitude less than the normal polarization maintaining fiber (PMF) configuration. The demonstrated filter presents a practical application potential in large scale laser driven facility.