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Yeah, you can just run up there ignoring the quest giver. HOWEVER - the environment will still kill you so you still will have to light the fires etc to survive up there. You can also just stand next to the torches along the path as well, that should stop you freezing to death, but bear in mind you will need to kill the mobs. The temple should be open to travel up to the higher level without the quest IIRC.
Xbox One - EU - EP/DC
Trying and failing to hold the walls of his Templar house up since 2015
The temple should be open to travel up to the higher level without the quest IIRC.
I did it pre-Summerset, and it was sealed off; I had to do the quest, but it only took me about 10-ish minutes. To me, that's worth more than figuring out how to parkour up there, which is probably possible... ^^ If I recall correctly, it's one of two base-game Skyshards that required the completion of a quest to get - the other was in the Mansion North of Vulkhel Guard, in Auridon.
@OP, just do the quest - it only takes about 10-ish minutes, and at any rate, you'll get a quaint little serving of XP at the end of it.
"One fine day in the middle of the night. Two dead Kings got up to fight. Back to back they faced each other, drew their bows... and stabbed themselves...".