。
She left the kitchen with the kettle boiling.
Literal
[topic-は] kettle [object-を] caused-to-boil [left-in-state-たまま] kitchen [path-を] left.
~たまま is the 'left in a state' marker — the action precedes a state that persists into the main clause. 沸騰させた is the past causative of 沸騰する ('to boil, come to a boil') — 'caused to boil.' Putting these together: 沸騰させたまま ('having put it to boil, in that state'). Note the implicit oversight: leaving a boiling kettle unattended in a kitchen is the kind of detail that signals distraction or hurry. 台所 ('kitchen') is one of two common words for kitchen, alongside キッチン (loanword) — 台所 has a slightly more traditional, domestic flavor.