I'd rather not execute a query in a shell script with an open text password.
mysql -uuser -hremotehost -pmypassword -e "update my_table set what_time = NOW()";
As written over at dba it is possible to configure your my.cnf file as the following:
[clienthost1] # Note: client + host1
and run it as:
Kudus to Derek Downey answer at DBA