Use the escaping rules from the jQuery selectors API as follows:
$('#root\\.SomeCoolThing')
From the docs:
To use any of the meta-characters (such as
!"#$%&'()*+,./:;<=>?@[\]^`{|}~) as a literal part of a name, it must
be escaped with with two backslashes:\\. For example, an element with
id="foo.bar", can use the selector$("#foo\\.bar").