It gets warm, how warm depends on the input voltage and the demand the power supply is under. The more overall work “work” it’s doing the warmer it will get. The metal tray is not a heat sink, it’s a case to protect the underside.
Keep in mind that if you remove the tray take care to insulate whatever is under it. If it touches anything it will short out the power supply. Removing the tray voids your warranty.