"The world will start COOLING DOWN in 2017"?
I gave a longer answer linked to a similar question in the comments above, I'll give a quick one here:


  There's a story going around the low-grade news factories that one Dr.
  David Evans . . .


Everyone knows there's a fair bit of "I know you are but what am I" in the climate change debate (if you can even call it a debate), but whichever side you agree with, David Evans is without question, actively arguing the skeptic side.  His position has been consistently in disagreement with man made climate change for nearly a decade, so anything of his you read, keep that in mind. 

He's made two climate "denier lists" here and here and he has been called out by skeptical science, here.    In another article related to yours, here, it says his work is "undergoing peer review", so for now, his calculations aren't publicly available or verified.


  . . . has predicted that the world will start cooling down in 2017


One problem here.  We're currently in an El Nino and 2014 was the warmest year on record (38% probability to some, but lets not go there) with 2015 likely to break that record and 2016 - too soon to say but the El Nino is expected to extend into 2016, so 2017 is an ideal year to predict cooling.  The global temperature often drops within a year after an El Nino ends, but this is a normal cycle and temporary and it has nothing to do with man made climate change.


  What would be the best way to show that he is wrong?


Well, a personal favorite, I'd go with something like: 

"He's just using a mathematical model to predict the future.  I thought you people hated mathematical models to predict the future. - 

You could also bring up this list of examples where David Evans has been wrong in the recent past.

But the more scientific answer to your question is that until his research is available and peer reviewed, then there's no way to disprove it, but there's also, no good reason to agree with it.   Without peer review and transparency, it's not science.   It's just a blog.