The Covers: I feel that they had the outlines of a person, like a black
Shadow, with green, yellow and red (blue?) backgrounds. These were the
Paperbacks. I read this probably around 2000-2004

The Plot: A museum curator has artwork stolen- or is sent to protect
Artwork- and falls in love/investigates the identity of a notorious art
Thief who also happens to be a rich collector? This could be me mixing and
Matching plot elements- but I think that's correct.

Names/Places/Scenes: I think the thief was named Alex, Alexandra,
Alexander (or maybe the heroine). I remember a scene where he (the thief)
Has the heroine trapped in the dark, in the museum, while guards are
Searching/looking around?

Title: To Catch A Thief? I feel that all three were sort of common catch
Phrases...

It sounds a lot like "The Thomas Crown Affair" to me.