How can I fix the picture on Grundig GU108047IV 47" LCD TV?

I've inherited it from a friend. When you switch it on at the wall (i.e. when it is cold), the picture is fine. Then after about 1 minute, the picture starts to break up then freezes (sound is fine) and then you can't watch it at all. It seems like it only works when its cold.

I don't know anything about TVs but I wonder if its something like a fan thats broken inside? And then maybe it gets too hot and the picture goes? I know its not the aerial as it does this elsewhere and the TVs that we have already work okay in the same aerial ports.

Do you have any ideas?