The problem with the transformer route, Keygrip, is that it produces 230 volts 60 Hertz, and if the TV minds about the mains frequency you're in trouble.
The data plate on the device will say what it wants. It may be 105-230v, 50-60Hz, or it may be anything between that and 230v 50Hz. The former just plugs in and will sort itself out. The latter won't like a transformer, and if it goes BANG the warranty won't be valid. In between are the devices that would be happy with a transformer.
12v power supplies and 12->240 converters aren't that big, these days, and most don't need cooling fans.