AbstractIn this paper, we introduce a new variant of the travelling salesman problem, namely the intermittent travelling salesman problem (ITSP), which is inspired by real‐world drilling/texturing applications. In this problem, each vertex can be visited more than once and there is a temperature constraint enforcing a time lapse between two consecutive visits. A branch‐and‐bound approach is proposed to solve small instances to optimality. We furthermore develop four variable neighbourhood search metaheuristics which produce high‐quality solutions for large instances. An instance library is built and made publicly available.