Scheduling a module to run at a specific time
Depending on how detailled your specific time is, you could still use hook_cron. For example, let's say the normal cron runs every hour, you could check date('H') in your module and only if it equals a predefined value, the cron function in your submodule will be executed.

function MYMODULE_cron() {
  if (date('H') == 3) {
    // this code will only be executed between 3:00am and 3:59am
    // do your stuff
  }
}