The system sounds an alarm when a condition is met where/that/in that the temperature exceeds a preset value.
I would like to know which of "where" "that", and "in that" is correct for the above sentence, although you may feel that the portion "a condition is met where/that/in" is unnecessary and needs to be removed
Yes, I would simply drop the phrase completely:
The systems sounds an alarm when [] the temperature exceeds a preset value*.
That seems the most natural to me.
However, if I were to keep the extra verbiage, I wouldn't use any of the phrases you suggest but something slightly different:
The systems sounds an alarm when a condition is met in which the temperature exceeds a preset value.
In the blog post "'Where' Versus 'In Which'," Bonnie Mills says this:
Many times, you can add a preposition before the relative pronoun “which” to make your sentence quite precise. For example, “The house at which I saw you” has a slightly different meaning from “The house in which I saw you.” If you use “where,” you lose the subtle distinction: “The house where I saw you.”
In this particular sentence, the alarm sounds when a condition is met—unlike in the blog post example that references a spatial location with where. At least one of the things that happens during this condition is that the temperature exceeds a preset value. So this temperature increase is part of the condition. (It may or may not be the only thing that happens). Because of this, in which more specifically conveys that sense.
