By Hookshot jumping off DampÃ©'s cabin you can get into Shadow temple early. Requires Hook/Longshot & Iron boots.
By performing an "invincibility glitch" hookshot jump, you can land on the seam and walk to the unloaded area in front of Shadow Temple.
By getting Death ISG and hovering off of a poe, you can get to the seam above the Graveyard and getinto the Shadow Temple with just a sword. This method is very difficult and precise, but is useful because it does require a Wrong Warp or Hover/Iron Boots.
By Farore's Wind Wrong Warping to the Nocturne of Shadow cutscene, you can get the song without any medallions. To warp to this cutscene set a warp either at Hyrule Fields -> Kakiriko Village or at House of Sleeping Talon -> Kakiriko Village.
Begin by setting a Farore's Wind warp point in Castle Town. Afterwards preform the death hole glitch. Use Ocarina items then return to the warp point you set previously which should take you to child Link Castle Town. Simply exit to the entrance area of Castle Town and you will be taken to the entrance of the Shadow Temple.