Jon Gosselin didn't have much to say after his Tuesday morning court hearing with estranged wife Kate.

When asked why he was grimacing, the dad of eight, 32, told Entertainment Tonight: "It's cold outside."

Jon's lawyer, Mark Heller, said, "We're hopeful. It's all we can say right now. We're very hopeful."

Kate, 34 -- who donned a bright pink shirt and jacket -- kept mum when asked if she'd provide accounting paperwork to prove to the court-ordered arbitrator that Jon took $230,000 from their shared bank account.

At the hearing, a judge advised Jon -- who dressed up in a dark suit -- and Kate to keep their split "private and amicable" for the sake of the kids. 

The couple -- who filed for divorce in June after 10 years of marriage -- are due back in court Oct. 26.