Extensive scientific research has found climate change is causing heat waves to become longer, more frequent and more intense.
Bangladesh's weather bureau says that average maximum temperatures in the capital Dhaka over the past week have been 4-5 degrees Celsius (7.2-9 degrees Fahrenheit) higher than the 30-year average for the same period.
Muslim worshippers gathered in city mosques and rural fields to pray for relief from the scorching heat, which forecasters expect to continue for at least another week.
"Praying for rains is a tradition of our prophet. We repented for our sins and prayed for his blessings for rains," Muhammad Abu Yusuf, an Islamic cleric who led a morning prayer service for 1,000 people in central Dhaka, told AFP.
"Life has become unbearable due to lack of rains," he said. "Poor people are suffering immensely."
Police said similarly sized prayer services were held in several other parts of Bangladesh.
The country's largest Islamist party, Jamaat-e-Islami, issued a statement calling its members to join the prayer services planned for Wednesday and Thursday.
'All linked to climate change'
Authorities ordered all schools last week to cancel classes until the end of the month.
The UN children's agency said it was "urging parents to be extra vigilant in keeping their children hydrated and safe" through the heatwave.
"The severity of this heatwave underscores the urgent need for action to protect children from the worsening impacts of climate change," UNICEF said in a statement.
Temperatures across Bangladesh have reached more than 42C (108F) in the past week.
"April is usually the hottest month in Bangladesh. But this April has been one of the hottest since the country's independence (in 1971)," government forecaster Tariful Newaz Kabir told AFP.
Kabir said fewer rainstorms than average for the period had contributed to the heat.
"We expect the high temperature will remain until the end of this month," he said.
Hospitals in the southern coastal district of Patuakhali had recorded local outbreaks of diarrhoea due to higher temperatures and the resulting increased salinity of local water sources, state medical officer Bhupen Chandra Mondal told AFP.
"The number of diarrhoea patients is very high this year," he said. "This is all linked to climate change."
