The union organisation said bosses should be happy with staff wearing vest tops and shorts rather than tights or jackets and ties during the hot spell.
Fans should be available in offices without air conditioning, it urged.
Firms should also supply cold drinks and allow employees to take frequent breaks, it said, as temperatures are expected to rise to 30C (86F).
Plans are already in place for some local trains to operate at reduced speed, and the TUC said that commuters and workers should be given flexibility at times of high temperatures.
"It is no fun working in a baking office or factory and employers should do all they can to take the temperature down," said TUC general secretary Frances O'Grady.
"Clearly vest tops and shorts are not suitable attire for all frontline staff, but those not dealing with the public should be able to discard their tights, ties and suits."
The Chartered Management Institute echoed the TUC's call for flexible working, claiming that many businesses underestimated the effect that weather conditions could have on output.
"It is therefore vital for employers to ensure they have business continuity plans in place to prepare for these situations, to ensure that productivity doesn't drop and that flexible working arrangements are on offer, should employees require these," it said.

16 January 2017 Last updated at 12:32 GMT
The ceremony is called the inauguration.
At the event, he will make a promise to do the best for the country and will give a speech known as the inaugural address.
There are a few traditions passed down, which he must observe on his inauguration day.
Leah takes a look at what's going to happen throughout the day...

Staffordshire County Council has a 99-year-lease on the Shugborough Estate in Stafford until 2065.
But now it wants the National Trust, which owns the Grade I-listed site, to take it back off its hands.
A spokesman for the National Trust has said it is exploring options for the management of the estate.
Mark Winnington, Staffordshire County Council's cabinet member for economy, environment and transport, said: "We are meeting colleagues at the National Trust to explore the feasibility of relinquishing our lease and passing the management of the Shugborough Estate to them."
The council said it expected to spend Â£650,000 this year maintaining and running the Shugborough Estate.
A spokesman said it took the lease on at a time when the National Trust was not as large. He said there was no threat to the building and the council would continue to manage it if an agreement could not be reached.
National Trust regional director Harry Bowell said: "At this stage the National Trust is working in partnership with Staffordshire County Council to carry out early-stage feasibility studies to explore options for the management of the Shugborough Estate.
"It is important to stress that no decisions have been made at this stage."
Shugborough was one of the manors of the bishops of Lichfield in the Middle Ages. The site was purchased in 1624 by William Anson, a lawyer. The current house dates back to 1694.
Staff should be allowed to dress down and work flexible hours during the hot spell of weather, the TUC has said.
[NEXT_CONCEPT]
On Friday, Donald Trump will officially become the next president of the United States.
[NEXT_CONCEPT]
The National Trust could take back responsibility for a 17th Century estate to save a council hundreds of thousands of pounds a year.