Temperature aware online algorithms for minimizing flow time

We consider the problem of minimizing the total flow time of a set of unit sized jobs in a discrete time model, subject to a temperature threshold. Each job has its release time and its heat contribution. At each time step the temperature of the processor is determined by its temperature at the previous time step, the job scheduled at this time step and a cooling factor. We show a number of lower bound results, including the case when the heat contributions of jobs are only marginally larger than a trivial threshold. Then we consider a form of resource augmentation by giving the online algorithm a higher temperature threshold, and show that the Hottest First algorithm can be made 1-competitive, while other common algorithms like Coolest First cannot. Finally we give some results in the offline case.