The documentation for the OS::Nova::Server resource indicates that the networks attribute is:

A dict of assigned network addresses of the form: {“public”: [ip1, ip2...], “private”: [ip3, ip4]}.

What they don't make clear is that "public" and "private" are just examples; the keys to this dict are the names of your networks. So, for example, in my environment I have a network named net0:

$neutron net-list|grep net0
| 18fc1b31-9b2c-4b6e-8dea-7e04bfd1eb43 | net0                              | 55c6da11-cfbe-4443-bb5f-19c4d0ea041a 10.0.0.0/24 |

If I deploy an OS::Nova::Server resource associated with that network:

 my_server:
    type: "OS::Nova::Server"
    properties:
      image: fedora
      flavor: m1.small
      key_name: lars
      networks:
        - network: 18fc1b31-9b2c-4b6e-8dea-7e04bfd1eb43

Then I can get the ip address like this:

outputs:
  server_ip:
    description: fixed ip assigned to the server
    value: { get_attr: [my_server, networks, net0, 0]}

Which will give me:

$ heat output-show ask server_ip
"10.0.0.34"