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.
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.
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.
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.
According to the (excellent) novelization of the movie, when Indy is under the Thuggee spell, he believes that there is a black snake coiled in his chest. When he is given an order by Mola Ram, if he tries to resist, the snake squeezes his heart until he complies with the order.
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.
The sacred stones that Mola Ram is searching for actually have some basis in fact. The real stones are called "lingham stones", and are symbols of Shiva. They occur naturally and are found in rivers throughout India.
In the novelization of the movie, Short Round believes that the elephant he is riding on is actually the reincarnation of his dead brother.