Talks between the airline and the government conciliatory service Acas are taking place today (Thursday 26 May) and on Tuesday 31 May.
The Unite union said more than 1,000 of its members voted in the ballot, and 74% backed industrial action.
Thomas Cook has reduced breaks for its cabin crew from one 20-minute break every six hours to one 20-minute break every 12 hours -- the minimum indicated in the UK Civil Aviation Authority's guidelines.
Unite says cabin crew should be entitled to at least two 20-minute breaks every 12 hours.
The union's National Officer Oliver Richard said: "Our members are deeply concerned about the impact these changes to rest breaks are having on inflight safety. Fatigue is a major contributory factor to accidents and slower response times when there is an incident."