The zootic viruses are present in wild and domestic livestock irrespective of climate change.
Sustained average warmer temperatures do challenge the immunity of some species, such as bats. So when humans handle the animals in wet markets, there might be a higher probability of transmissions from sick animals -- but that's only a guess.
But diseases in general could become more prevalent due to climate change. At places like the South Pole, it's too cold for bacteria to multiply easily, while in the tropics many diseases spread with incredible ease.
No, I don't think they are related.. The reverse may be true... that the increase in frequency and ease of travel means people are more mobile, which increased transmission.. So, less travel would cause less global warming and decreased likelihood of pandemics.