Australia's white-ball players flew out on Wednesday for the tours of Zimbabwe and South Africa, the squad including several of the Test stars ahead of next month's series.
The South Africa red-ball series will be the launching pad for Prime Video's newly-announced fourth series of The Test documentary.
The Test team has not played in the country since the 2018 series, which was headlined by the ball-tampering controversy that cost Smith 12 months of cricket.
Hazlewood insisted this week he did not foresee next month's series being as heated, but could envisage a world where Smith arrives with extra motivation.
It comes after the 37-year-old averaged 110.57 in his return series during the 2019 Ashes, following his year-long ban stemming from sandpaper-gate.
"I think so," Hazlewood said when asked if Smith would have a point to prove.
"We saw him come back at Edgbaston that time after 12 months out and get 100 in both innings, so he has that in him.
"He always wants to do well. Look out if he has that sort of feeling again."
Smith's importance to Australia could be heightened next month, with low scores and seaming wickets predicted given the early-summer conditions.
The 2018 Cape Town Test followed a dramatic opening start to the series, which included David Warner and Quinton de Kock having to be separated in a stairwell during the first Test in Durban.
Kagiso Rabada was then charged with making physical contact with Smith when celebrating a wicket during the second Test, before a ban was overturned on appeal.
"I can't see it going like that," Hazlewood said.
"I haven't seen a series go like that since that one. It was just so over the top, almost from ball one.
"I don't know whether it was two teams at boiling point who had been on the road for a long time and were mentally drained and fatigued."
"Everything was really over the top. I can't see any issues like that again."Hazlewood has warned that barbs from the crowd will not impact Australia during the tour, while noting crowd abuse is easier to hear in South Africa than at home or in England or India.
Alex Carey, who was the No.1 target for English fans in 2023 following the stumping of Jonny Bairstow, insisted he would not be fazed by a hostile environment.
"I learned not to worry about it," he said.
"In sport there is always going to be a level of rivalry and someone is going to be a villain and a hero. Nation to nation, someone is going to cop it.
"It's part of sport and (it's about) not letting it affect us. I don't think it really has.
"We've been (to South Africa) twice for ODI series and it's a normal level of banter. We'll wait and see but from my point, learn to embrace it and laugh it off."
The South Africa series will be the first filmed for the 2027 version of the fly-on-the-wall Test docuseries, which will also take in next year's India and Ashes tours.
"Hopefully we play ball for the doco and win a few games and get the right results and make it a good season," Hazlewood said.
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