Is it permissible to delay making up a missed Fajr prayer for an hour after waking up at ten to heat water due to illness?

Scholars differ on whether making up a missed prayer (qada') is obligatory immediately or can be done at leisure. If one cannot use water for wudu' or ghusl except by heating it, then one must wait enough time for it to heat up so that it can be used without harm. There is no sin upon someone who sleeps before the time of prayer enters, even if they strongly expect that they will miss it, because they are not addressed by it at the time of their sleep.