Air carrier Captain reported an ATC directed rejected takeoff due to previously cleared aircraft rejecting takeoff prior to the Captains' takeoff on the same runway. The Captain stopped their aircraft and cleared the runway; then proceeded to take off after brake cooling.

Narrative

Cleared for takeoff behind Aircraft Y on Runway XXL at ZZZ. Early in our takeoff roll; Tower advised us to cancel takeoff clearance. I immediately rejected the takeoff and noted 85 KIAS (prior to the 100 knots callout). Rejected Takeoff (RTO); auto brakes engaged and brought the airplane to a stop just short of Taxiway 1. Tower asked us clear the runway at the next reverse high speed (1). We cleared the runway and were instructed to hold short of 2 on 3 and advise intentions. While we were clearing the runway; I noted the Aircraft Y exiting the runway at the far end and reporting to the Tower that they had rejected their takeoff due to a high Interstage Turbine Temperature (ITT). We completed the Rejected Takeoff QRC. FO started computing Brake Cooling Time while I spoke with Flight Attendants (FAs) and to the passengers. We computed a conservative cooling time; considering taxi length; of 45 minutes. I called Dispatch advised of the above. After discussing fuel; weather; etc.; Dispatch agreed that we should be okay to continue at the completion of the brake cooling period. Called Chief Pilot and had similar discussion adding reporting requirements. Chief Pilot agreed that we should be okay to continue. During the cooling period; I discussed Tarmac Delay considerations with the FO and kept the FAs and passengers informed. Nearing the end of the cooling period; we obtained new takeoff data; re-ran all pre-takeoff checklists; started engines and departed XXL without further incident. Tower thanked us for our help. Also; during cooling period; FA 1 called to advise that her neck and back were a little sore; but she was okay to continue. Lead FA confirmed that she; and everyone else; were okay to continue.