Phil Bentham, 59, and Mark Cremer, 55, are understood to have died on their rounds on August 12 and 13 respectively.
Coroners said their deaths were of natural causes and will not be subject to inquests.
Royal Mail bosses launched their internal probe after mounting pressure from the Communication Workers Union (CWU).
Mr Cremer is said to have collapsed and died on an "undulated" round with a "reasonably high" gradient.
He was based at the Lancing Delivery Office in West Sussex and had worked for Royal Mail for almost 20 years.
The postie had known underlying health conditions and was found slumped at the end of a pathway by a resident.
He died shortly after an ambulance was called.
Stepdad-of-four Mr Bentham, of Barrow-on-Furness in Cumbria, died at the end of his round having recently returned to work after 17 weeks of shielding from Covid-19, according to union chiefs.
The CWU is calling for a joint investigation into the service's "severe weather risk assessments" to protect workers in the future, and to see if more could be done to take into account employees' underlying medical conditions.
It said in a letter: "As branches would expect, representations have been made to Royal Mail at the most senior level following these deaths.
"Specifically, concerns have been raised in relation to the important health and safety issues that need to be addressed in respect of working outdoors in excessively hot weather conditions.
"In particular, the issue of sun safety and dehydration risks to the outdoor workforce has been escalated several times over the last few months.
"We have of course also taken up this matter previously when similar hot conditions have been experienced."
Mr Bentham's Ormsgill councillor Bill McEwan added: "It's absolutely right that an investigation is carried out if that's to protect the other workers.
"My goes out to the family and this will give them peace of mind.
"It means his death leaves a good legacy for other workers."
A Royal Mail spokesman said: "We are waiting for the results of our own internal investigations and any medical findings before commenting further in order to avoid unhelpful speculation.
"The health and safety of our people is our number one priority at Royal Mail.
"We provide clear guidance aimed at protecting our people's safety, health and wellbeing as they carry out their work. We also ensure access to drinking water."