choke control


I have a 1997 xi Sportrak.

The choke comes on ok but seems to open before the engine has warmed up and it runs like a pig for abut 10 minutes, when warmed up it's ok.
I think that the choke control is governed by water temp
Do you guy's think a new thermostat will cure it, ie, if the spring has got weak and is opening too early allowing the warm water through and opening the choke. It's done about 59k