We propose and demonstrate for the first time, to the best of our knowledge, a thermally controlled all polarization-maintaining (PM) fiber Lyot filter. This filter is implemented in an all-PM mode-locked fiber laser to achieve wavelength tunability. When operating in the single-wavelength tunable mode, the center wavelength can be tuned across a range from 1546 nm to 1571 nm. Furthermore, the laser can also operate in a dual-wavelength mode with center wavelengths at 1545 nm and 1571 nm. The temperature sensitivity achieved in our all-PM fiber Lyot filter is 0.602 nm/°C, which is over 46 times higher than other fiber-based filters such as a fiber Bragg grating filter (0.013 nm/°C). This highly stable and versatile wavelength-tunable all-PM fiber mode-locked laser is a promising source for various applications requiring wavelength tunability and/or dual-wavelength output, such as coherent Raman microscopy and dual-comb spectroscopy.