Auckland Transport says the city's train network will not be up to full service for another month.
The disruption is likely to continue, Auckland Transport public transport director Stacey van der Putten says.
"It may well be the new normal for the next month or so. What's important to understand is that trains are running - it's the key message here. Trains are running, on some lines there might be a slightly reduced frequency."
Auckland's mayor is demanding the city's transport bosses explain why the trains keep being disrupted.
Auckland Transport said 88 trains were cancelled across its commuter network on Monday due to a range of problems - not just the heat.
While some trains could not run because of speed restrictions imposed to stop tracks buckling, it said other trains were cancelled due to crew shortages and a breakdown.
In a letter to the heads of KiwiRail, Auckland Transport and Auckland One Rail, Wayne Brown described the transport agencies' communication as "muddled" saying they often blame each other over rail network failures.
"The frequent disruptions on the Auckland train network have become unacceptable," he said.
"Aucklanders have reached the end of their patience with train cancellations due to the weather, signal failures, crew issues or other excuses."
Brown said his office would arrange a meeting with the heads of transport this week, and had invited Minister of Transport Simeon Brown or his representative to attend.
"I'm asking you three to meet with me to explain how these disruptions keep happening, and what is being done to both fix it and quickly restore public confidence," he said.
"Aucklanders need to be confident that their public transport system is reliable, and able to cope with a mild summer's day."
He said of Monday's cancellations that it "cannot be a surprise to any of you that Auckland gets warm in February".
"The communication between all three of your agencies has been muddled, often blamed each other, and been described to me as an "omnishambles". I could use other language to describe it."
KiwiRail's David Gordon said trains had to travel at half their usual speed over four kilometres of rail, which needs to be upgraded to prevent over-heating.
He said the agencies are working hard to fix the problems.
Government weighs in
Transport Minister Simeon Brown, who is also the Minister for Auckland, told reporters he had called KiwiRail into his office on Monday after overheated tracks led to the cancellations.
"Incredibly concerned and frustrated on behalf of Auckland commuters," he said.
"The reality is there needs to be far better coordination and communication in these situations when that does become a problem and I've made that expectation very clear to Kiwirail."
"I raised my expectations and made them incredibly clear, but Auckland Transport's also responsible, the operator's also responsible, the expectation is really clear that all three agencies which are responsible need to be working together."
"They can't just let this all happen in such an uncoordinated way."
He said the good news was areas where the tracks had been worked on recently were working fine, but the agencies responsible "need to be working a lot harder around dealing with these issues".
Minister Brown said he or a representative would be present at the meeting with the mayor.