Confirmation of the deaths came the same day that weather authorities said July was China's hottest month since records began six decades ago.
China is the world's biggest emitter of the greenhouse gases that scientists say are driving climate change and making extreme weather more frequent and intense.
Heatwaves this summer have scorched parts of northern China, while heavy rain has triggered floods and landslides in central and southern areas.
This week's downpours were triggered by Typhoon Gaemi, which moved on from the Philippines and Taiwan to make landfall in eastern China a week ago, with hilly, landlocked Hunan province hit particularly hard.
More than 11,000 people were evacuated from the city of Zixing after some areas endured record rainfall of 645 millimetres (25 inches) in just 24 hours, state news agency Xinhua said on Tuesday.
Many roads connecting townships in the Zixing area were temporarily cut off, which also affected the power supply and communications infrastructure.
State broadcaster CCTV said Thursday that the disruption was mostly over.
"Initial findings show that there have been 30 deaths and 35 are missing," the report said, adding that search and rescue efforts were ongoing.
Premier Li Qiang visited two villages in Zixing on Thursday "to learn about progress on disaster relief and the extent of the damage", Xinhua reported.
As well as searching for the missing and restoring infrastructure, Li said efforts must be made to "guard against secondary disasters like mountain torrents and mudslides" according to state media.
Xinhua had reported Tuesday a landslide on Sunday had killed 15 people in Hunan province.
- Historic heat -
Last month was "the hottest July since complete observations began in 1961, and the hottest single month in the history of observation", the national weather office said Thursday.
It said the average July air temperature in China was 23.21 degrees Celsius (73.78 Fahrenheit), exceeding the previous record of 23.17C in 2017.
The mean temperature in every province was also "higher than the average for previous years", with the southwestern provinces of Guizhou and Yunnan logging their highest averages, the weather office said.
It forecast that temperatures would continue to climb in eastern regions this week, including in Shanghai, where a red alert for extreme heat was in place on Thursday.
"Next week will be more of the same. It's like being on an iron plate," one user of the Weibo social media platform wrote in response to the megacity's heat warning.
Another quipped: "It's so hot. Did Shanghai do something to anger the gods?"
The nearby city of Hangzhou may hit 43C (109F) on Saturday, which would break its all-time record, the weather office said.
Middle and lower reaches of the Yangtze River would likely see daily temperatures fall no lower than 30C, it said.
- Extreme summer -
The news came little more than a week after the Earth experienced its warmest day in recorded history.
Preliminary data from the Copernicus Climate Change Service showed that the daily global average temperature was 17.15C on July 22.
That was 0.06C hotter than the day before, which itself broke the all-time high temperature set a year earlier by a small margin.
China has pledged to bring emissions of carbon dioxide to a peak by 2030, and to net zero by 2060, but has resisted calls to be bolder.
It long depended on highly polluting coal power to fuel its massive economy but has emerged as a renewable energy leader in recent years.
Research released last month showed that China is building almost twice as much wind and solar energy capacity than every other country combined.
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