Yesterday the union questioned the safety of the old buses on days above 40 degrees Celsius.
The union said many of the buses, which have come back into service after being mothballed, lacked air-conditioning or had systems that broke down in hot weather.
The Government says buses without air-conditioning are only running on the shortest routes from the city to North Adelaide and Woodville stations along the Gawler and Outer Harbor lines.
Union secretary Ray Wyatt met with Transport Minister Patrick Conlon earlier today to discuss drivers' concerns.
He says he is now satisfied that measures are in place to guarantee the safety of drivers.
"The Government has established to me that the contractors have the duty of care, as do the Government, as do I, that they have extreme heat policies in place that will ensure that driver safety is paramount in all of this," he said.
"In very difficult circumstances they are working extremely hard in an environment and climate that changes daily.
"We have committed to monitor it, especially on extremely hot weather days."
Mr Wyatt says while drivers have been informed of their rights, there will be no unauthorised mass walk-off.
"The Transport Workers' Union is not in a situation where we would be engaging in unlawful industrial action," he said.
"Each and every individual employee has a right under the OH&S act to remove themselves out of a hazardous, dangerous situation."
The union earlier called for the replacement of evaporative air-conditioners which it said were staying switched off because of the threat of Legionnaires disease.
Mr Wyatt says he now accepts that that is not feasible.
"The only solution for it would be to kick them off the top and put new air-condition on the old buses," he said.
"The timeframe to air-condition these things with after-market air-condition would take substantial time and if we're talking about a month it will be all over."
Mr Wyatt says he will have further meetings with Transport Services Minister Chloe Fox when she returns from leave in two weeks.
Yesterday the union challenged the Transport Minister to take a ride on one of the buses in the hot weather.
Mr Conlon dismissed that gesture as an 'empty stunt' but says he is still happy to comply.
"Yes it is a stunt but I will say this, right, just to put this all on an even keel. We had meaningful discussions. We had honest and robust discussions with each other," he said.
"If the union believes there's some use in that we'll do it but what I guarantee you is there won't be any cameras there.
"There will not be any cameras there. It will not be a media stunt."
Mr Conlon says passengers are being offered free water on hot days and nothing more can be done to improve their journeys.
"It is a once-in-a-lifetime closure of the entire rail system while we rebuild it," he said.
"I defy anyone to do more than you can. We're doing all that we can.
"We simply haven't got the option of buying a whole load of buses for a month.
"We inherited a bus fleet where half the buses weren't air-conditioned and we inherited trams that were older than Bob Hawke where the air-conditioning was a leather strap to pull the window down."
Mr Conlon says there is no chance the railway station will reopen ahead of schedule.
"The truth is that when you do these sorts of works on very old infrastructure you often get surprises under the ground in terms of where wiring and where utilities are," he said.
Click this link to read the orginal article on ABC News.