The Absa Premiership giants played to a goalless draw at FNB Stadium on Saturday.
"The heat affected us," Khune told his club's website.
"We usually play at night, only seldom during the day. The pace at which we wanted to move the ball around should have been much faster.
"However, the high temperatures made that nearly impossible. Both teams didn’t play at their best as a result of the immense heat.”
Khune was nevertheless pleased to register a sixth straight clean sheet against Pirates.
“Every goalkeeper wants a clean sheet. However, credit must also go to our defence. Both teams came up with their tactical battle plans. There were box entries, but both defences did well.”
Amakhosi, who are ahead of Golden Arrows at the summit on goal difference, next 'host' topflight newcomers Baroka FC at Durban's Moses Mabhida Stadium on Wednesday night (kick-off: 19h30).
Chiefs have 14 points from seven matches - six points ahead of Bakgaga.