Ms Green said third quarter results marked a "crucial milestone" in the company's turnaround plan and meant that it was no longer having to resort to "crazy" offers to get rid of unsold holidays.
Figures showed pre-tax losses down 6% to £79 million for the three months to the end of June while the company pointed to a separate measure excluding finance costs that saw it return to the black. Revenues were up 5% to £2.35 billion.
Ms Green said it was too early to tell how the heatwave had affected sales - amid fears that travellers are reluctant to pay for sunshine breaks this summer when they can bask in warm weather at home.
She said: "We are a big business, one that is becoming more and more stable servicing the needs of our customers. It is hard to imagine that a little bit of good weather is going to distract us from that strategic transformation."
Profit margins improved as bookings remained flat despite a 6% cut in capacity, and average selling price increased. Ms Green said consumer confidence appeared to be "slowly but surely" returning.
Bookings in continental Europe excluding France were up 1%. In France, where capacity has been slashed by a fifth, they were down by 12%. Popular destinations for Thomas Cook included Turkey and Tunisia - despite political upheaval in those countries - as well Spain and Greece. Upheavals in Egypt had not had a significant impact in an area where business had already been scaled back.
Ms Green, who became chief executive last year, highlighted an earnings measure that excludes finance and restructuring costs that showed an improvement to £1 million profit from £23 million losses in the same period last year.
Thomas Cook staved off collapse last year after a rescue deal with lenders. In May it unveiled a £425 million fundraising with shareholders as part of a wider £1.6 billion refinancing deal. It is cutting costs in the current financial year by £170 million. Today it said net debt had been halved from £1.1 billion to £452 million.