An inquest last year ruled there was a "missed opportunity" for Army chiefs to step in before Private Jason Smith collapsed in temperatures in excess of 50C (122F) in Iraq.
The 32-year-old, from Hawick in the Borders, had repeatedly told medical staff he was feeling unwell due to the soaring temperatures after being deployed to Iraq in June 2003.
He collapsed on August 13 that year with a fatally-high body temperature of 41.4C (106.52F). He was taken to hospital but suffered a cardiac arrest and died.
Assistant coroner for Oxfordshire Alison Thompson, recording her findings at the end of the five-day hearing, said: "When climatic conditions deteriorated in August and the number of heat casualties increased, there was a missed opportunity to intervene."
Those in charge could have "become more rigorous in monitoring individuals" when temperatures soared, making sure they were treated for their symptoms and had enough rest, she added.
An original inquest was held in 2006 but a second was ordered by the Supreme Court after Pte Smith's mother Catherine successfully applied for a new public hearing, complying with the European Convention on Human Rights.
Mrs Smith has now reached a settlement with the MoD and also received an apology over her son's death.
She said: "It has been a long fight for information and I am glad that the Ministry of Defence has finally acknowledged that there was a missed opportunity to intervene, and the risks that contributed to Jason's death could have been reduced.
"I have continued to fight because no other families should have to go through what I have been through.
"I have been reassured that changes have been made as a result of Jason's death."
The MoD said it has reduced the risk of soldiers suffering heat-related injury since Pte Smith's death.
The apology by David Evans QC, on behalf of the MoD, said: "We apologise unreservedly for the death of your son, Private Jason Smith, whilst he was on active service in Iraq on August 13 2003.
"The Ministry of Defence acknowledges the coroner's findings that the risk of Jason's death could have been reduced by adherence to the policy in place at the time, including in relation to climatic monitoring, better advice on hydration, medical treatment, casualty reporting and the availability of air conditioning.
"There was a missed opportunity to monitor and intervene, and become more rigorous in the monitoring of Jason.
"We apologise for the loss of Jason's medical records and the distress caused to you as a result.
"We acknowledge more effort should have been made to locate them and it was unacceptable that some records were only produced on the last day of evidence at the second inquest.
"We acknowledge Private Smith's commitment and dedicated service to the Territorial Army for over 10 years and on active service in Iraq on behalf of his country in 2003."
Mrs Smith has been represented by the Hodge Jones and Allen legal firm.
Solicitor Clair Hilder said: "I am glad that we have been able to reach a settlement with the Ministry of Defence and that Mrs Smith's case has finally come to a conclusion. Particularly important to Mrs Smith was the apology which has been secured. It is just disappointing that it has taken so long to obtain and that the Ministry of Defence has fought her every step of the way."