My Roku stick was getting the overheating message. This has happened in the past with other sticks. I first detached the stick and put it in the freezer for a while, then attached an HDMI extender to see if that will solve the issue. In the meantime, I checked the serial no and signed onto ROKU to see if is flagged ... but lo and behold, it's not show up on my account. I know it's activated because I'm getting all my apps.
Where did you check the serial number? The number written on the stick itself may be a Device ID and not a serial number even if it's labeled SN or "Serial number". You can always find the real serial number under Settings->System->About.
It's in the settings on the stick itself, along with the model, software version et.al.
When you go to Settings / System / About on the Roku, is the email address shown the same one you used to log into your account at Roku.com?
yes