I replaced the batteries and then had to switch back to Rec. to continue recording. All parameters were accepted and a new recording started. But as Andreas Sutter already wrote: It will be difficult to get exactly the same image section again. But if this is not so important, changing the battery is no problem.
I couldn't use a power supply unit because the camera was mounted on top of a tree...

No, the camera is without power without a battery.
I recommend a power supply unit anyway, as changing the battery without moving the camera is hardly possible.