"I want to personally doff my hat to you for your calmness in this interview. I almost threw my phone at the wall 4 times," Neesham wrote.
Shaw replied "thanks".
But since the interaction, Plunket has 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".
Plunket then commented on the number of Neesham's Twitter followers, saying the "number is a lot less than the runs or wickets he's got".
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.