That's what I ended up doing ... even though mine wasn't a stream, once I realized water was leaking past the gasket, I figured the odds of it sealing tight again were not good. I figured after 366k miles it was probably due for a new one. Once the coolant was drained, it was pretty easy to take the housing on and off. Plus the gasket is relatively cheap. You may want to replace the little bypass hose under the t-stat housing while you're at it, if it looks old.
I think the worst part of the job was getting that A/C bracket back on. Hopefully yours won't be such a pain, but mine would an absolute bear to get the holes lined up again. I ended up spraining my neck in the battle. 
Good luck! 
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1987 300D, arctic white/palomino--314,000 miles
1978 240D 4-speed, Euro Delivery, light ivory/bamboo--370,000 miles
2005 Jeep Liberty CRD Limited, light khaki/slate--140,000 miles
2018 Chevy Cruze diesel, 6-speed manual, satin steel metallic/kalahari--19,000 miles
1982 Peugeot 505 diesel, 4-speed manual, blue/blue, 130,000 miles
1995 S320, black/parchment--34,000 miles (Dad's car)
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