The first match begins at the Basin Reserve in Wellington on Friday, four days after New Zealand won the deciding one-dayer to retain the Chappell-Hadlee Trophy.
The second test is at Hagley Oval in Christchurch.
Hesson is predicting different conditions than in the ODIs in Auckland, at Wellington's Westpac Stadium and in Hamilton.
"These wickets, they were good but they were certainly on the slower side, so they brought in some different challenges," he said.
"The way the Basin and Hagley have played suggests there will be a little bit more life in them."
Skipper Brendon McCullum, who in Wellington will make a record 100th consecutive test appearance before ending his international career in Christchurch, is preparing for "a bit more of a tinge of green" at both venues.
"There should be plenty of sideways movement," he said.
"I expect probably a little more pace and bounce than what we've seen in the one-day wickets but, geez, they served up three pretty great games as well."
Australia were twice bowled out for under 200 in the one-day series and skipper Steve Smith said his batsmen hadn't adapted well enough to the New Zealand conditions.
He blamed poor shot selection for a lot of their woes.
"The summer at home, the batters played particularly well," he said.
"Over here, we haven't stepped up."
The tourists will go into the opening test without a warm-up match in whites, but Smith didn't see lack of preparation as an issue.
He said players nowadays were used to playing in all three forms of the game and it was a case of adjusting quickly.
"I assume the wickets will have a little bit in them, so we're going to have to adapt accordingly."
