Ange Postecoglou hailed Celtic for putting on a show in difficult conditions after they recorded the biggest away victory of his reign.
Celtic navigated the heatwave and Rugby Park's plastic pitch to thrash Kilmarnock 5-0 and go top of the cinch Premiership on goal difference above Rangers.
There was little doubt about the outcome after Kyogo Furuhashi finished off a penetrating move inside seven minutes and the points were wrapped up by half-time thanks to Jota's 30-yard strike and Jenz Moritz's acrobatic finish.
Celtic rediscovered an extra gear after some second-half changes and substitutes Carl Starfelt and Giorgos Giakoumakis both netted, the latter with an overhead kick.
Postecoglou said: "We spoke about it before the game. It wasn't the easiest of conditions for our boys to play football both in terms of the temperature and the pitch.
"To the players' credit they kept their discipline and focus and committed to our style of football.
"There were plenty of excuses for us to just look at this game as 'three points and get up the road' but we still wanted to put on a performance and I was pleased that the players did.
"I thought the quality of our goals was excellent and the quality of our general play attacking-wise was good."
Postecoglou admitted he enjoyed lapping up the post-match celebrations with the away fans.
"It looks like they have enjoyed themselves even prior to the game, and rightly so," he said. "It's always good because this is a game where it can turn into a bit of an ugly game, you win it and it's not memorable in any way.
"But we don't want to miss opportunities to give our fans some special moments and today was one of those days. Some of our goals really pleased our fans and for us it's a really important message in terms of us sticking to our football."
Starfelt netted his first goal for Celtic when he finished at the second attempt at close range on his first appearance of the season following a hamstring injury.
"He has worked really hard to get himself back to a position where he is available again," Postecoglou said. "Credit to him, he is a really good pro.
"I am really pleased for him to get a goal - he has been trying really hard. It was probably the ugliest of the five but probably the most significant."
Kilmarnock manager Derek McInnes was "embarrassed" by the scoreline.
"For all the talent Celtic have, I was disappointed with the level of goal we lost," he said.
'Two corner-kicks, three goals in the six-yard box. I need to see the Jota goal again but my first thought is we should have saved it.
"Other than the Giakoumakis overhead kick, there were no real goals defined by the difference in quality. It was more our responsibility and lack of willingness and resolve to deal with that situation. That's what I'm more concerned about.
"It still shouldn't be 5-0, even though we're not ready to take on a Celtic, that's what I'm disappointed with.
"I'm embarrassed by it, but we need to dust ourselves down and hopefully by the time we play the Old Firm next time around we're more settled into the Premiership and better equipped to get a better result than we were today."
There was an added blow with on-loan Reading defender Jeriel Dorsett limping off in the first half.
When asked how he was, McInnes said: "Not good, he heard a pop and I think it's ligament damage of some sort.
"It's too early to make assumptions, but I think he'll be out for a period of time, which is far from ideal.
"We were looking forward to working with him, he's a young boy who is powerful and quick.
"We've still got time in the window to address one or two areas we're clearly needing. Hopefully it's not too bad for the boy but it doesn't look too good in terms of the next few games certainly."