No, bulb of a thermometer can’t be made of an adiabatic wall. In thermodynamics, a wall which does not permits thermal interaction is referred as adiabatic wall and a boundary wall that allows heat exchange between the system and surroundings is referred as diathermic wall. To measure the temperature of a body, the bulb of a thermometer is put in contact with it. Within sometime, the bulb reaches the body's temperature allowing us to determine the temperature of body. If the wall of a thermometer is adiabatic, then there will be no exchange of heat energy between two systems and temperature of the body cannot be measured. Therefore, the bulb should be made of diathermic wall not adiabatic wall.