A spirit never entered Cole. Cole is a manifested spirit that took the shape of a human boy he sympathized, but he is not a possessed body. That's what makes him so strange. From his codex entry:
"As Solas insists that he is a spirit made manifest in the form of a young man, not a demon possessing an unwilling victim, I concede that he may not be malicious."
And some helpful Dorian banters:
Dorian: You're not possessing a human body, Cole? You... actually look like that?
Cole: Yes.
Dorian: But a spirit's true form is always monstrous, or at least unnatural.
Cole: The world doesn't make sense to them. It's too real. That's why they look wrong.
Dorian: And... this is how you want to look?
Cole: I want to help. Looking doesn't matter.
Dorian: Can you change your form, Cole? If you wanted to look like something else?
Cole: But I don't want to look like something else.
Dorian: Hmm. There are magisters who'd be ecstatic if they could summon a demon who could pass for human.
Cole: They would use it to hurt people.
Dorian: You're right about that. They would.
Dorian: Cole, are those real clothes, or-?
Cole: They're real. What else would they be?
Dorian: I thought maybe you'd conjured them, like your physical form.
Cole: Do you conjure yours? Is that why they look like that?
Dorian: Never mind, forget I said anything.
Basically, Cole crossed the Veil like demons and spirits can, but instead of manifesting as something more twisted, like a rage demon, or a wraith-like creature as we saw other spirits do in Crestwood, he took on a more human form, inspired by the dying boy he crossed over to help in the first place.
I hope that makes sense, gah. xD
On topic: Flemeth is, like, so great, guys. ;D