I was using a friends laptop and decided to boot into an install of tinycore on a flash drive. This laptops battery is already pretty much shot because it is left plugged in all the time no matter what the use, and before I booted into it the level was at about 60%, which means about 40 minutes in windows. When I booted into tinycore, there was only about 10 minutes before it shutdown completely. I noticed the fans were on high and the air coming out was rather hot, but why does that happen?
First, leaving a laptop plugged in all the time is the best case for battery life. Simply put, with the laptop plugged in, the battery manager can do whatever it thinks is best for the battery life, whether that's charging it, floating it, or discharging it. With the laptop unplugged, there is no option but to discharge the battery, whether or not that's best. (Batteries are completely different from what they were a decade ago. The old rules no longer apply.)
My bet is that tinycore either doesn't have adequate power management support or it's not enabled. Another possibility is that power management is set to low (or disabled) in the BIOS but those settings are overridden with the Windows power management settings. Linux will follow the BIOS if not specifically configured with an override as well.