This is tough one. If you have an older mercury type thermostat, behind the cover theirs a small copper pointer that points to some numbers. This is your heat anticapator. This setting has to match your milliamp draw of all the controls on your furnace. If set to low it over heats and fools the thermostat into thinking its satisfied. Move the point to a higher setting in little increments. Hope this works for you. Can't help with the vibration without hearing it.