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The set's starting point is the conclusion that the temperature rises only when the AC is turned off.
When the AC is turned off, the temperature rises linearly, reaching the temperature at the time it was turned off in one hour.
The temperature rises in two instances,
From 0:00 to 0:30, it rises from 26 to 31, so by 1:00, it would have reached 36 degrees, meaning that the temperature at 0:00 would have been 36 degrees Celsius.
From 1:00 to 1:30, it rises from 26 to 30, so by 2:00, it would have reached 34 degrees, meaning the temperature at 1:00 would have been 34 degrees Celcius.
Calculating either of these would have been enough as we have the starting temperature at 23:00 at 38 degree celsius. Since the temperature decreases linearly, we can find the temperature at every instance using another data point.
Drawing out the temperature outside, we get:

We can see that the AC was turned on at 0:30, 1:30 and 23:00.
We do not know about the status at 23:30
We are to count the times after 11:01 pm; hence, turning on the AC at 23:00 does not count.
Hence, the answer should be 2 or 3.
But in the final clue, we are given that POWER mode was used longer than REGULAR mode.
Since there are 4 periods of 30 minutes each, the combinations possible are POWER-3, REGULAR-1, and POWER-4, REGULAR-0
If the AC were on REGULAR mode at 23:00, it would have functioned for 1 hour, and the power mode would have also functioned for 1 hour (total), which would go against the final clue.
The following would be the cases.

But there were three instances of activation between 11:01 and 1:59
Hence, option d would be the correct answer.