Staff should be sent home if their workplace gets hotter than 30C, according to a group of MPs.
Labour MP Linda Riordan has tabled a petition calling for the new law, and has attracted the support of 17 colleagues.
As Britain swelters in a heatwave, the motion warns that employees in workplaces ranging from industrial bakeries to school classrooms are often subjected to temperatures which can "impact seriously on their health and well-being".
Consequences of overheated factories and offices can include "discomfort, stress, irritability and headaches... extra strain on the heart and lungs, dizziness and fainting and heat cramps due to loss of water and salt", and the resulting reduction in alertness and attention spans can contribute to workplace accidents and fatalities, said Riordan.
The TUC has backed a legal maximum temperature of 30C - or 27C for those doing strenuous work - and Riordan's motion urges the Government to adopt these levels in law.
The motion has been signed by 12 Labour backbenchers, two SDLP MPs and one MP each from the Liberal Democrats,
DUP and Plaid Cymru.
It came as officials sent out heatwave health warnings and four people died in water as Britain continued to swelter during the hottest spell of weather for seven years.
After five consecutive days of 30C-plus temperatures, the Met Office issued a "level three heat health watch" for London and the South East and advised "alertness and readiness" for those in the North West and North East of England.
Meanwhile, police and fire chiefs reiterated warnings about escaping the heat by swimming in open water after four people died at lakes in Norfolk, a river on the Shropshire/North Wales border and the sea in Cornwall.
Forecasters said Britain was in the midst of its first prolonged heatwave since 2006 and predicted that Wednesday could again break the record for the warmest day of the year, with temperatures as high as 32C (89.7F) in parts of England.