We demonstrate that the extraordinary transmission of terahertz radiation through semiconductor gratings of subwavelength apertures can be switched completely by varying the temperature. The enhanced transmission, which is due to the resonant tunneling of surface plasmon polaritons that can be excited in semiconductors at terahertz frequencies, is controlled by thermally modifying the density of free carriers. The transmission through metal gratings cannot be switched in the same way since the carrier density is temperature independent. Thus semiconductors offer an interesting alternative to metals in enhancing the transmission of electromagnetic radiation.