Germany became the first country to reach the milestone of 100 World Cup matches and marked the occasion by thumping Cristiano Ronaldo-led Portugal.

Mueller bagged the Germans' seventh World Cup hat-trick in total -- more than any other nation -- with Argentina second on four.

"Thomas did really well up front and he constantly tore holes in the defence," enthused Loew after the Group G clash.

"He is a very unorthodox player and you can't really predict his lines of running, but he has one aim and that is 'how can I score a goal?'

"That makes him so dangerous, especially in the box."

A decisive first-half saw Germany race into a 3-0 lead in Salvador as Mueller converted a penalty, then fired home their third on the stroke of half-time after Mats Hummels scored with a header.

Mueller, who normally plays as a winger or attacking midfielder for Bayern Munich, wrapped up his hat-trick with a scrappy effort in the dying stages as Ronaldo endured an afternoon to forget.

"The whole team played incredibly compactly and hardly gave anyway any chances to counter-attack," added Loew.

"When we went 3-0 up, it was important to hold the ball and play more economically.

"Jerome Boateng did really well against Ronaldo."

Ghana await the Germans next in Recife on June 21 and with high temperatures expected for the 1600 kick-off local time (1900 GMT), Loew says changes may come.

Hummels is an injury concern after being helped off with a thigh problem and Loew has said he will weigh up his options over the next few days.

"We will now look at the team set up," said Loew.

"Ghana has an incredible physique, they are very robust, with very fast players.

"The heat conditions will demand a lot of us.

"Mats Hummels had a knock to the thigh, but I assume that it wasn't too serious."

Loew said it was a particularly good day for Germany after news broke on the morning of the match that ex-Formula One world champion Michael Schumacher has come out of a lengthy coma.

"It's very good news, we are all elated of course," said Loew.

"Led by (Schumacher fan) Lukas Podolski, we all really crossed our fingers for him and the fact he has taken the next step is great."

German Chancellor Angela Merkel visited the team dressing room after the match, as she has done on previous occasions, which also boosted Loew's squad.

"She gave a little speech to say how nice it was that we won, especially after such a long trip here," said Loew.

"There was a lot of applause.

"We always like it when she comes to see us, she is always a nice guest to have."