Trivia: Just like Indiana was named after George Lucas' dog, Willie was named after Steven Spielberg's dog and Short Round was named after screenwriters Bill Hyuck and Gloria Hatz's dog.
Trivia: When Indiana Jones is confronted with the two swordsmen and goes to draw his gun to repeat his easy kill from the first Indy movie, listen to the music. It's the same music that was played in Raiders of the Lost Ark in the marketplace shortly before he pulled his gun on the big twirling swordsman.
Trivia: Kate Capshaw and Steven Spielberg met each other on the set of Indiana Jones and the Temple of Doom. They are now married and have seven children together.
Trivia: Due to a severe back injury, Harrison Ford was not even present for most of the conveyor belt scene. It was mostly done using his stunt double. Harrison was added in later with close ups and reactionary shots.
Trivia: There was only one red sequined dress for Kate Capshaw to wear during filming. This practice is literally unheard of today. There are typically multiple pieces of movie wardrobe produced in case of damage, staining or loss.
Trivia: Roshan Seth and Amrish Puri who play Chatter Lal and Mola Ram also appeared together in Richard Attenborough's epic film Gandhi in 1982.
Trivia: The little boy, Ke Huy Quan, didn't initially intend to try out for Short Round. He was merely accompanying his brother who auditioned for the character, but Ke Huy called out so much advice to him that he caught the directors' notice.
Trivia: Something a lot of people don't necessarily pick up on. Temple of Doom is actually set before "Raiders".
Trivia: When the first sacrifice victim is being lowered into the lava pit, he is chanting "Om Nam Shiva" over and over. This translates very roughly as "Universe, Earth, Shiva," though the words themselves refer to complex concepts. This is a mantra from a Hindu practice called Shiva Yoga. Shiva Yoga also involves the use of Lingham stones, like the ones Indy is after in the movie.
Trivia: Harrison Ford injured his back when he was fighting with the Thuggee inside his suite in Pankot Palace, who was trying to choke Harrison but Harrison flips to knock the guy off. It took two weeks for Harrison to come back from his herniated back injury (after surgery).
Trivia: In the novelization of the movie, Short Round believes that the elephant he is riding on is actually the reincarnation of his dead brother.
Trivia: Kate Capshaw got a black eye when Ke Huy Quan (Short Round) hit a Thuggee, who was trying to capture Kate before she could get on the mine cart, with a stick (which was actually balsa wood) that broke in half and part of it hit her in the eye.
Trivia: Star Wars Reference: Indy charges after the guards with a sword just before going on the bridge, then has to make a quick retreat when they chase him. Remember Han Solo and the chase of the stormtroopers on board the Death Star? Harrison Ford is one brave man...
Trivia: Some of the action scenes in in this film were actually written for 'Raiders of the Lost Ark', but were dropped and incorporated into this one.
Answer: This is conjecture, but it seems the general function of setting Temple of Doom before Raiders of the Lost Ark is that it helps set audience expectations that the two movies are self-contained episodes. For instance, Karen Allen has said she wasn't disappointed about not being asked to return because she'd already been told that the next installment was being set in the past before her character is reunited with Indy. Conversely, since we're already aware Raiders makes no mention of the events of Temple of Doom, we know we shouldn't necessarily expect any further installments to continue directly from prior movies' storylines regardless if they are set forward in time.
TonyPH