Following the show, Plunket hit back at Neesham.
"Well, Jimmy I feel like throwing my bloody phone at the wall often watching the Blackcaps," Newshub reported.
Plunket criticised the cricketer for speaking out about climate change while flying "all over the world".
"Is that why you catch planes all over the world to play cricket Jimmy?"
He continued to berate the cricketer, seeming to suggest that Neesham's career is "completely pointless, yet burns up tonnes of carbon".
Over the following three days, in a series of posts in response to other users' tweets, Neesham has slammed Plunket's show.
"I'd rather put toothpicks under my toenails and kick a door than listen to that drivel in my day to day life," Neesham posted when asked if he had actually tuned in to the show.
Another Tweet about Plunket read "I've actually had him blocked for months, maybe even a year. I cultivate my timeline to keep it free of inflammatory racism, bigotry etc."
Finally, on Friday, Neesham responded to a request by Plunket to join him on his radio show with another indirect lashing of his show.
"He's trying to drum up a massive controversy to become briefly relevant and get one retweet and 5 likes," Neesham tweeted.
Neesham has been outspoken about the effects of climate change. The 29-year-old recently told the BBC he feels it is important to have at least a passing knowledge of global social issues like politics and climate change.