Assistant head coach Winkler has joined up with the coaching team at Town after the West Yorkshire outfit contacted Barnsley on Wednesday afternoon to ask permission to speak with him.
The Reds granted that request, with Winkler having a buy-out clause in the deal he signed when he become No 2 at Oakwell last summer.
Stendel confirmed that he has a target in mind in his native Germany to come in as a permanent replacement for Winkler, but will be assisted by Tonge in the last three games before the situation is reassessed.
Stendel, whose side host Rochdale on Saturday, said: “I think we have found a good solution with Dale in the coming days. We spoke a long time about what I expect from him. I think he is a good option for us and the team. I am happy he is involved with our team.”
On the longer-term situation, he added: “Maybe we sign another coach, but Dale will support us. I will think about a coach from Germany, but at the moment I am happy with Dale.”
Winkler links up with Jan Siewert, who he has known since they undertook their coaching qualifications together with the pair working together at Rot-Weiss Essen, where Siewert spent a spell as coach and Winkler acted as sporting director.
On the departing Winkler, Stendel added: “Andy and Jan worked together at Essen and he told me about this offer and I said: ‘ok’. I said I wanted him to stay, but from the outside, this is a big chance for him to work in the Premier League.
“I am disappointed he left and I think we worked very well in the first seven months together. But it is the way in football. Players leave and this time, Andreas has left the club.”