This kettle has a base, right? There are a number of possible causes of you problem.
There could be a problem in the connections from the base to the kettle - cleaning them up might help.
It could be a thermal fuse - though in this config I wouldn't think it would be in the base.
It could be the heating element in the kettle - that would likely be non-replaceable.
It could be the temp sensor in the kettle - tha would also likely be non-replaceable.
Bottom line, you will need to trace it out with a multimeter to find the disconnect.