You could use Screen Sharing to do that reasonably well. The built in version doesn't do fullscreen by default, so if the iMac is running a lower resolution than the TV's, it will be in a smaller window on your TV. Third party VNC clients (which is the protocol Screen Sharing uses) can do fullscreen. This would be simpler in many ways, including no need to use a second keyboard and mouse to use the iMac from the other room.
Your iMac likely supports a higher resolution than the TV does. The maximum standard TVs today use is 1920x1080, and if your iMac is an Intel Core i3 or i5, its own display is at least that high of a resolution. Which model of iMac do you have?
If your iMac is running at least Leopard (10.5), then both machines have Screen Sharing built in. It can be accessed from the Finder, but as often as you would like to use it you should go to Macintosh HD > System > Library > CoreServices and drag it (the icon) to your Dock. That will create the shortcut to get to it easily. As I noted before, the built in Screen Sharing VNC software doesn't do full screen, but third party VNC software can. Both machines do not need to be using the thrid party VNC software, just the one viewing - in this case your Mac mini. Chicken of the VNC is a popular free one, fairly easy to use:
For more info about how to set up Screen Sharing and how to use the included application:
Note that you will have to use the settings in System Preferences, regardless of what VNC software you use. Both systems will need to have Screen Sharing settings enabled.