zonetemplate=$(cat << SETVAR
info here
other things here
SETVAR)
The above is all you need, note that if you have variables you need to escape the $ with a so you then have $ otherwise the variables will be substituted which is probably often not what you want so be aware of that.
To echo the variable above/write it to a file with proper formatting you need to do something like this:
echo -e "$zonetemplate" >> file.zone
The -e preserves the formatting and the double quotes are also needed around the variable or things won't turn out as expected.