"Clean the entire unit by soak
"Clean the entire unit by soaking in radiator cleaner (oxalic acid power in water). After soaking a few hours, dry off a little bit and liberally use penetrating oil around the sleeve edges, top and bottom. Sometimes this alone allows you to slowly tap the thermostat out along with the sleeve.
If you have not yet gotten it out, drive the thermostat out with a block of wood (destroys the thermostat of course). This leaves a very thin gap above the sleeve. If you are lucky you may have a small puller that will engage the upper rim of the sleeve in the gap. If not, use a screwdriver blade and use many light taps with a mallet around and around the edge of the sleeve driving it out slowly. Sometimes you get lucky and can press it out using the "windows" in the sleeve. Just work slowly to not damage the housing.
If the sleeve is reluctant to go back in the housing, liquid soap is a good lubricant with a flat block of wood as a tapping surface."