Yesterday morning I found my N810 reboorting and then turning off. The day before is was just in idle state connected with Wifi. Then I connected the charger and it continued rebooting. Then I disconnected the charger and after 1 day I connected the charger and was able to turn it on without rebooting.

How can I disable this reboot bot ?

I'm thinkin' your battery has reached the end of its useful service life...
Both my N800 and 810 exhibited this behavior that was eventually solved by installing a fresh battery.

Are you sure that replacement of a battery stops a reboot-bot ?
Normally when the battery gets poor, the charge just lasts shorter and that is not the case with my N810. A charge of the battery lasts nearly as long as when I bought it in 2008.
I think it is a software induced reboot bot which is a bug in the firmware.

The N810 charger is unable to charge very degraded/aged batteries, it panics and aborts. The System watchdog notices that the battery management software is no longer running, which is a critical problem, and reboots the device.

Hence, when the battery gets too old/worn, the N810 is stuck in a reboot loop when on charger..

Your issue doesn't sound like the battery-reboot issue though.

This is a known bug in the BME driver. If you search the forums, you can find suitably indignant, angry, pitchfork-and-torch-wielding posts about how Nokia screwed us there.

Also, you can search the bugtracker for BME and you'll find the sordid details there, as well.

Without a software fix, yes, getting a new battery is the answer.