Jason Sudeikis and Olivia Wilde are hot and cold -- one minute they're duking it out in court, the next they're all kumbaya in public ... and this time, it's the latter they're showing.

The exes were spotted attending their son's soccer game together in L.A. Saturday, and wouldn't you know it -- they actually looked super happy and chill around one each other ... even sitting in the stands side by side, and giving one another a huge on the way out.

It's interesting they were acting this way out in the open ... for a couple reasons, actually.

For starters, we saw similar behavior from Jason and Olivia earlier this year -- when they were hugging it out after apparently leaving some sort of meeting they were both at. At the time, it seemed everything between them was water under a bridge ... but it wasn't.

Since then ... we know they've been waging war behind the scenes, filing court paperwork in their ongoing custody battle ... with Olivia recently taking home a big W. As we reported ... a judge finally ruled that their case will be heard in L.A. and not in NY (where JS wanted).

Remember, they share two young children together ... Otis and Daisy, who are 8 and 6, respectively. The family had lived in the Big Apple for a while -- but the courts have now decided, once and for all hopefully, that their primary residence is, in fact, in Los Angeles.

Perhaps this latest outing is them actually turning a new leaf and waiving the white flag -- or, it could just be optics. However cynical you are will dictate where you land.

One other reason this is kinda neat to see ... Jason is very famous for playing Ted Lasso in the self-titled Apple show, which is a huge hit -- and whose third season just started.