Australian super funds on average are managing climate change risk well, with Local Government Super topping a list of the world's top-500 asset owners.
But the Future Fund, Telstra Super and Asgard scored poorly on this year's Global Climate Index.
On average, Australian funds come in second behind Norway in the Assets Owners Disclosure Project's annual report.
Local Government Super reclaimed top spot in 2014/15 after slipping to second last year.
The Climate Institute says that's because, among other things, the fund calculates its portfolio-wide emissions and under-weights carbon-intensive stocks.
The index ranks the 500 biggest pension, insurance and sovereign wealth funds on their management of risks associated with climate change.
It measures transparency, risk management, low-carbon investment, active ownership and incentive chain alignment.
Climate Institute CEO John Connor told AAP this year's index is a mixed bag and shows Australians should be questioning their super funds' climate change positions.
He believes the Future Fund - which ranks 96 - is doing very little in terms of climate risk management and that should concern all Australians.
The index assigned nine funds a Triple-A rating.
If all funds were meeting this standard the world would be much closer to solving climate change, the report said.
However, the report says the gap between the world's best and worst is widening.
The index comes as the institute calls on the federal government to "unambiguously" confirm its commitment to the internationally-agreed goal of limiting global warming to two degrees.
The group is concerned the two degree goal was notably absent from the recent energy white paper and issues paper on post-2020 targets.
However, it was mentioned in the intergenerational report and in a tweet by Environment Minister Greg Hunt.
"We're getting mixed messages," Mr Connor told AAP.
In its submission to the taskforce on post-2020 emissions reductions targets, the lobby group says Australia must cut emissions by 40 per cent by 2025 and achieve net zero-emissions by 2050.
The government will release its post-2020 target in June and is watching trading partners to determine Australia's fair share.
A Future Fund spokesman later told AAP changes in technology, regulatory settings and economic conditions, including as they relate to climate change, were incorporated into the construction and management of the portfolio.
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