Pending the filing and final disposition of proceedings for review under sections 536.100 to 536.140, the agency may stay the enforcement of its order and may temporarily grant or extend relief denied or withheld. Any court in which such proceedings for review may be pending may issue all necessary and appropriate process to stay or require the agency to stay the enforcement of its order or temporarily to grant or extend or require the agency temporarily to grant or extend relief denied or withheld, pending the final disposition of such proceedings for review. Such stay or other temporary relief by a reviewing court may be conditioned upon such terms as shall appear to the court to be proper. No such stay or temporary relief shall be granted by a reviewing court without notice, except in cases of threatened irreparable injury; and when in any case a stay or other temporary relief is granted without notice the court shall then make an order, of which due notice shall be given, setting the matter down for hearing as promptly as possible on the question whether such stay or other temporary relief shall be continued in effect. No such stay or other temporary relief shall be granted or continued unless the court is satisfied that the public interest will not be prejudiced thereby.