Connecting pgAdmin3 to Postgres on Heroku
Thanks to @araqnid on Stack Overflow for the answer here.

Quoted Verbatim from there:

Open the "Properties" of the Heroku server in pgAdminIII and change the "Maintenance DB" value to be the name of the database you want to connect to.
The default setup is suitable for DBAs et al who can connect to any database on the server, but apparently that isn't true in your case.

This worked for me!