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As explained in Tarkin by James Lucerno the Jedi temple was built atop a Sith shrine.

This was slowly corrupting the power of the light side and clouding the vision of the Jedi who lived there, this would most likely make it less painful for Sidious to be there.

It is also mentioned in the book Darth Plagueis how Palpatine is able to shield himself so he doesn't show any force sensitivity.

One might conclude that this talent would work the other way and shield him from any effects the light side might have on him. It would also explain why the Jedi council could not sense him.

Using only legends sources -

In the New Jedi Order book Traitor by Matt Stover it is revealed that the Jedi temple was built atop a "wellspring of dark energy"

This would have corrupted the power of the light side and clouded the vision of the Jedi who lived there, this would most likely make it less painful for Sidious to be there.

It is also mentioned in the book Darth Plagueis by James Lucerno how Palpatine is able to shield himself so he doesn't show any force sensitivity.

One might conclude that this talent would work the other way and shield him from any effects the light side might have on him. It would also explain why the Jedi council could not sense him.

As explained in Tarkin the Jedi temple was built atop a Sith shrine.

This was slowly corrupting the power of the light side and clouding the vision of the Jedi who lived there, this would most likely make it less painful for Sidious to be there.

It is also mentioned in the book Plageius how Palpatine is able to shield himself so he doesn't show any force sensitivity. One might conclude that this talent would work the other way and shield him from any effects the light side might have on him. It would also explain why the Jedi council could not sense him

As explained in Tarkin by James Lucerno the Jedi temple was built atop a Sith shrine.

This was slowly corrupting the power of the light side and clouding the vision of the Jedi who lived there, this would most likely make it less painful for Sidious to be there.

It is also mentioned in the book Darth Plagueis how Palpatine is able to shield himself so he doesn't show any force sensitivity. 

One might conclude that this talent would work the other way and shield him from any effects the light side might have on him. It would also explain why the Jedi council could not sense him.

The Jedi temple was built atop a Sith shrine.

This was slowly corrupting the power of the light side which would most likely make it less painful for Sidious to be there.

It is also mentioned in the book Plageius how Palpatine is able to shield himself so he doesn't show any force sensitivity. One might conclude that this talent would work the other way and shield him from any effects the light side might have on him. It would also explain why the Jedi council could not sense him

As explained in Tarkin the Jedi temple was built atop a Sith shrine.

This was slowly corrupting the power of the light side and clouding the vision of the Jedi who lived there, this would most likely make it less painful for Sidious to be there.

It is also mentioned in the book Plageius how Palpatine is able to shield himself so he doesn't show any force sensitivity. One might conclude that this talent would work the other way and shield him from any effects the light side might have on him. It would also explain why the Jedi council could not sense him