The emergency destruction system aboard the USCSS Nostromo operated on a ten-minute delay, with an initial five-minute fail-safe window during which the process could be aborted. However, after these five minutes had elapsed, the meltdown of the ship's core was irreversible and could not be stopped.
https://avp.fandom.com/wiki/Emergency_destruction_system
Reading that, it takes 5 minutes for the coolant not operating to let the powerplant go into meltdown, and after 5 minutes, this is irreversible.
That is why the timer to cancel the self destruct is also 5 minutes - beyond that there is no stopping of what destruction comes with a powerplant meltdown.
....
In addition to what Valorum said (in the comments), it is generally accepted that anything generating power, generates heat, and needs cooling to not meltdown or explode. Space in itself can be very hot, or very cold, (Note the International Space Station has a very active cooling and heat dissipation system running) but in this context its probably that without cooling systems on, the ship is a very inhospitable place to work
Also, in the script, they make references to the life support requiring coolant to operate:
(transcript) Ripley:
We're gonna need coolant for
the air support system.
You two go down, get all
the coolant you can carry.
In light of the answer that Valorum linked to in the comments, it is more likely that the coolant was for power plant, and at 5 minutes to go, with coolant switched off, meltdown was irreversible.
For reference, some spaceships operated with explosive self-destruct devices at the time the movie was in production. This was separate to the FTS, range safety self destruct for launchers, which still operates today (Russians just turn off the engines for self-destruct during launch-phase, but the Soyuz operating from Kourou have FTS added).
https://scifi.stackexchange.com/a/268181/140676
Ripley first turns off the cooling system and then turns it back on (when she decides she does not want the ship destroyed which I do not understand)
Ripley decides she does not want the ship destroyed because originally she was going to leave in the escape craft, leaving the alien to get blown up along with the ship - but after setting the self-destruct and heading towards the escape craft, she found her route blocked by the alien, so she needed more time (than the self-destruct was going to give her) in order make a new plan to get to the escape craft.