Can leaking radiator hoses cause problems in the transmission? What else?

I've got a 2007 Ford Explorer Sport Trac, had the radiator replaced last July, needed to take to a closer garage because I was afraid of way transmission was acting. They left a message saying all radiator hoses were original and basically leaking evweywhere. And there's a bunch of other problems. Something with the thermostat. They're trying to figure out if tranny is totalled. Waiting for a call back. Just wondering what problems can ensue with bad radiator hoses.

I believe it can cause a problem in keeping your engine cool.

I would find another shop.
I don't believe it's 'leaking everywhere'.

Power to the people.

I'd be cautious with a garage that clams radiator hoses leak everywhere. It may be just a sales pitch in order to generate sales, that old line about being OE. My hoses are OE from 2003 and they aren't leaking anywhere. The thermostat is another thing they are trying to pump up sales, it works until it doesn't, there's not much in between that could go wrong there.Bottom line is the hoses have nothing to do with the trans. Wish you would have told us about what the trans was doing.

Radiator hoses have absolutely nothing to do with the transmission. The only relation they have is the radiator itself that usually has a closed cooler circuit for the trans fluid built right in. It's a heat exchanger within a heat exchanger if you will. Tread carefully with this shop if I were you because I think they want to take you for a ride a little bit.