Dylan da Silva, aged 20, died on Saturday at the Curry Cabral Hospital in Lisbon several days after falling ill during a Commandos training course.
He was awaiting a liver transplant due to organ failure caused by the heat-related complication.
His death comes a week after a fellow soldier on the same course died from the same condition.
The army said the training courses have been “restricted” until ongoing inquiries into the deaths are completed. Dylan Silva’s funeral took place on Monday.
Meanwhile, Portugal’s Minister of Defence, José Azeredo Lopes, said this week that courses run by the army Commandos are to be suspended until the conclusion of an internal inquiry into the death of two soldiers.
Minister Lopes had earlier told Lusa News Agency that he was considering intervening, but only after the conclusion of the two investigations currently underway into the deaths - an internal inquiry and a criminal inquiry by public prosecutors. Last week the army had stated that despite the death the training exercises would continue, but that they would be adapted to the high temperatures.