This is called evaporator box. Has this been dismantled from the system? If yes, then mask the refrigerant inlet and outlet lines & clean it with detergent along hot water. Do not expose it to high pressure water since these fins are highly fragile and would bend straightaway. If this is still attached to the system, then mix detergent with water in a bottle and spray all over. Leave it for an hour and then wash it with water. Thermostat switch is placed at the end opposite to the expansion valve or exit.
