Plenty of indirect ways.
For example, McCoy thinks they are aging 30 years per day. Assuming McCoy or Scotty is in his forties, that's probably a maximum of two days of action, or else our heroes would look like dried-up mummies. Might be three, but McCoy is probably being wildly optimistic in saying that they have "less than a week" to live.
Also, in the day of the competency hearing, Spock says Kirk sent a message to Starbase 10 "this morning", and although we don't witness him doing so, we'd expect him to have sent the message almost immediately after deciding not to leave the Gamma Hydra system.
Stardates in the episode increase by a whopping 101 units between Kirk's two log entries, but we can't really trust Kirk at this point - he probably said "SD 3579.4" when he should have said "SD 3479.4" or something.
No more than three days by McCoy's diagnosis, then, and probably somewhere between one and two. All the action could easily fit within two days, and could well be squeezed in a shorter time as well.
Timo Saloniemi
