First I would do a SMC reset. Follow this Apple T/N: [https://support.apple.com/en-us/HT201295|Resetting the System Management Controller (SMC) on your Mac].
SMC has a few different functions. So while it manages battery charging and battery power management. This part of SMC does not involve the temperature management side of things.
I do strongly recommend putting the battery back in (replacing it) only because when you don't have it present it doesn't take much to pull out or cause a power disconnect from the power adapter. The way the system was designed the battery would fill in the power disruption. Think of it this way your laptop has a built in UPS!