All planets orbiting the star will fly away tangentially towards outer space .
Temperature will drop slowly.
According to Newton's First Law, every planet would continue to move, with its orbital speed, in the direction of motion at that instant, with near-zero acceleration.
When compared with the Sun's centripetal attraction, the
attraction on any planet, by any other, is negligible.
So, Newton's First Law is applicable. Every planet would continue to
move with its own system of satellites ( if any ), rings ( if any) with
the velocity, at that instant.
The planet's attraction would soon bring to its fold its own satellites
and rings and other fliers that are in its proximity..
In the case of the Earth, this speed would be about 29.78 km/s with
near-nil acceleration. In my estimate, it would draw Luna into its fold,
in 3 to 4 hours.
The individual planet's attraction stays. In our case life would
extinct, within a short time. .
Let us not have any phobia of this sort. This apocaypse might
happen billions of years from now.
Remember, our star Sun would annihilate its constituents long
before ( 4 billion years from now, for inner planets ) its self-
annihilation ( some billions of years later ).