I'm projecting the same level of likelihood (not certainty) as one of the experts in coronaviruses (not just general expert in epidemiology)
Third of third of common colds are caused by coronaviruses and they they show clear seasonal pattern (SARS don't because it's mostly human-animal transmitted). You can't say for certain that it's the case for this virus but it's very likely.
Not only can I not find a source corroborating your statement by John Nicholls beyond this forwarded email of a transcript of a call that allegedly happened weeks ago, but what you stated ("This virus will burn itself out in May when temperatures rise.") is not even an alleged quote from him. It's a summary by the person who typed this up. The closest thing Nicholls (allegedly) said is this:
In regards to temperature, the virus can remain intact at 4 degrees or 10 degrees for a longer period of time. But at 30 degrees then you get inactivation. And High humidity the virus doesn’t like it either. That’s why I think Sars stopped around May and June in 2003 – that’s when there’s more sunlight and more humidity. The environment is a crucial factor. The environment will be unfavourable for growth around May. The evidence is to look at the common cold – it’s always during winter. So the natural environment will not be favourable in Asia in about May.
Totally different from "it will burn itself out by May", which multiple experts across multiple fields increasingly consider uncertain at best.
Third of third of common colds are caused by coronaviruses and they they show clear seasonal pattern (SARS don't because it's mostly human-animal transmitted). You can't say for certain that it's the case for this virus but it's very likely.