Install the lm-sensors package and check the temp of your system. The fan is trying to catch up after the shutdown allowed heat to build up (fan cuts off immediately, but temps then spike as internal heat is no longer being removed). I'm on my third motherboard (HP Compaq) because of inadequate cooling. Consider an external cooler also to force more air through your system and keep the air flowing a minute after shutdown.
Also a good idea to check for any BIOS/firmware updates from HP. Many of those had to do with fan control. Don't know what hardware the lm-sensors supports. My 7 yr old laptop is supported by sensors.
To list the packages available run
apt-cache pkgnames |grep fan
I see no jupiter, but there are some other to try out.