Sith/Dark Jedi in Jedi temple possible

It would be possible, but highly difficult, and a Dark Jedi/ Sith would already have to be quite knowledgeable in the Force in order to do so. Anakin Skywalker was able to disguise his Dark Side tendencies at the Temple, as was Jorus C'Baoth, and Palpatine was routinely meeting with Jedi as part of his duties as Chancellor. Kyp Durron had trouble disguising his Dark Side tendencies from Luke Skywalker, and Luke was nowhere near as knowledgeable or as powerful as the Jedi of the Old Republic.

EDIT:

In response to the OP's edit, I must point out that no, this is not possible. Jedi and Dark Jedi don't work side-by-side, except under extreme duress, such as the Abeloth incident.

The Jedi would most likely never knowingly allow somebody to train in the Dark Side within their temple. This answer is mostly expanding on Richard's point that the Jedi and Sith have competing values.

Here are Mace Windu's thoughts on the Clone Wars and the Dark Side:

Spoilers for Shatterpoint

Note that the jungle Windu is referring to was on a planet that was steeped in the Dark Side because of lots of war and killing. In this jungle, the Dark Side drove Windu's former padawan, Depa Billaba insane and she fell from the light. In short, the Jedi's true enemy is the Dark Side itself.

Here are the views of Darth Plagueis:

Spoilers from Plagueis

Further down (talking about ruling the galaxy and other stuff):

So as you can see, if Darth Plagueis tried to waltz into the Jedi Temple and declare that he wanted to study the Dark Side there, I think Mace and the other Jedi would have a problem with that.

What about the Dark Jedi?

Let's take a look at a few prominent Dark Jedi:

Asajj Ventress, Aurra Sing, Set Harth, and Depa Billaba were all Jedi that fell to the Dark Side. Ventress and Sing were responsible for the deaths of many Jedi. Harth was responsible for the deaths of a couple civilians. Depa was charged with crimes against civilization because of her actions on Haruun Kal.

Suffice to say, it is improbable that the Jedi would allow any of them to study at the Temple at all.

There are many other Dark Side practitioner's as well, but they most likely wouldn't get the nod either.

Let's recap:

1. Darksiders tend to not like the Jedi.
2. The Dark Side can corrupt Jedi.
3. The use of the Dark Side is generally incompatible with Jedi beliefs.
4. I highly doubt Coruscant and Korriban had a foreign-exchange program for students.

No, as answered in some depth already.

The Jedi and Sith are mortal enemies. The Jedi thinks that the Sith are the worst thing in the galaxy. Even Jedi Master Mace Windu is about to kill Palpatine because he thinks a Sith Lord is too dangerous to be kept alive and stand trial, even when Palpatine is unarmed and helpless (even if he isn't helpless, Windu thinks he is and that is what matters).

Revan, Jedi turning to the Dark Side before going back to the light, is basically shunned by the Jedi in the novel 'Revan'.

In the Bane trilogy:

The Bane trilogy also mentions Sith Holocrons, which the Jedi searches for, in order to hide them in their restricted section of the Jedi Archives. And

Those short examples, as well as the previous answers, makes me believe that there is no chance that the Jedi would let Dark Force-users freely roam the Jedi Temple.