"tput: No value for $TERM and no -T specified " error logged by CRON process

Something in the script is calling the tput binary. tput attempts to inspect the $TERM variable to determine the current terminal so it can produce the correct control sequences. There isn't a terminal when cron is running so you get that error from tput.

You can either manually assign a TERM value to the cron job (likely dumb or something similar to that) or (and this is likely the better solution) you can find out what is calling tput and remove that call.

The cron daemon is run by 'root' user in its own shell. By default, cron will append a system mail sent to the user running the script (that's why you see the sender as 'root' in the system mail). The 'user' is the user you were logged in as when setting the crontab. The mail will contain console and error messages. On Ubuntu, the mail file is viewable at /var/mail/<username>.

If no $TERM variable is set, cron will emit a tput: No value for $TERM and no -T specified error in the mail file. To stop these errors, set the $TERM variable using TERM=dumb (or another available terminal in your system, like xterm) in the crontab. The toe command will show you the terminfo definitions on the current system. If you lack that command, you can see the raw data in /usr/share/terminfo on most Linux systems.

Even though you have stopped the errors, you may still get appended system mail with console messages. This file will fill up like a log over time, so you may want to stop these messages. To stop cron system mail, set the MAILTO variable using MAILTO=""

So your crontab might look like:

MAILTO=""
TERM=xterm

* * * * * sh /path/to/myscript.sh

You can view the crontab (for the user you are signed in as) with 'crontab -l'.