Had a 2.0 GLI petrol Omega. Beautiful solo car - roomy, smooth and well equiped. However when towing spent more time on the AA recovery than the road as it constantly over heated. Prior to this had two Carlton 2.0 GLI petrol cars and they were the same - damn nuisance regarding the constant over heating whilst towing
I used to tow with an Omega estate 2.5 petrol automatic. it never overheated but did tend to get quite hot on hills (for example Telegraph Hill outside Exeter). Apart from that a very good tow car (although a little thirsty) that served me well towing for six years. My wife now has it.
As an aside a friend of mine had a Frontera 2.2DTi- the same diesel engine as the Omega and he had no end of trouble with it overheating and blowing head gaskets - he had to be recovered from Spain.
We're now on to our third Omega. Why so many? Because it is simply the best towcar we have had in almost 25 years of caravanning. Better even than the Volvos we had years ago. Ours have all been petrol engines, though, so I can't comment on your particular model.