Currently, when you follow a link to a chat room, you'll automatically join the room. This means, everyone in the room sees who's just entering that room.
For me personally, this is almost never the desired behaviour. I want to read the contents of the room, joining a room is an entirely separate decision for me. I almost never join a room unless I intend to participate in the discussion.
This behaviour is for one surprising, I don't think everyone expects that they'll be publicly joining a particular chat room just by following a link. This is made even worse by the "convert comments to chat" function, which leaves chat links scattered on the main sites. I can't just read the converted comments, I have to join the chat because it's the only link there (unless I manually try to find the room). For me this means that I never actually follow the links to chat unless it's something really important to me.
Joining a chat room is an active action to me, not something that should automatically happen without the user's consent. It has privacy implications, other users get notified that you're looking at that chat room at that specific point in time. It can also provoke reactions, suddenly I'm greeted by someone I don't know because they noticed I entered that room. As I'm a moderator they might also suspect that there is some kind of trouble which caused me to enter that room.
Following a link to a chat room should not automatically make you join that room. The easiest way would be to just redirect to the transcript, but that could be confusing for people that aren't familiar with SE chat. The other option would be to still go to the live chat page, but without joining chat. So the bar at the bottom would have a big "join this chat room" button instead of the message box.