Kristy Scott filing for divorce from her husband Desmond Scott doesn’t seem to be bothering him one bit -- 'cause just days later, he was spotted getting hot and heavy with another woman ... and TMZ’s got the proof!

Catch the late-night Sunday clip -- Desmond looked very comfortable at Houston bar Sante, with a woman parked on his lap as the two went full make-out mode like a pair of teenagers.

It’s pretty raunchy -- behavior better suited for behind closed doors -- but these two were fully locked in, completely ignoring the room as they put their intimate display on full public view.

As we reported, just 2 days earlier, TMZ broke the story that Kristy filed for divorce in Harris County, Texas -- citing alleged infidelity and making it crystal clear there’s zero chance of reconciliation.

It’s still unclear if the woman in the video is the one at the center of those claims, but Desmond did break his silence once the split went public, admitting he made "choices" he’s "not proud of."

We reached out to Desmond ... he declined to comment.