[2] In 2001 he received his Doctor of Theology from the Philosophical-Theological School in Vallendar with a dissertation on Hans Urs van Balthasar, the Swiss Catholic theologian.

[2] On 28 February 2014, Cardinal Joachim Meisner, Archbishop of Cologne, resigned[4] and Heße was elected diocesan administrator.

Co-consecrators were Archbishop of Cologne Cardinal Rainer Woelki and Norbert Werbs, Auxiliary Bishop of Hamburg.

[7] In a September 2015 plenary council, the gathering of German bishops and other clergy focused most of the discussion on the European migrant crisis that had begun earlier that year.

[8] The plenary elected Heße as the German bishops' special envoy to the migrant crisis, which placed him in charge of the dioceses' response efforts.

which were set aside as aid for refugees both in and outside of Germany, and 800 unused church-owned buildings, which were designated as housing for migrants.

[8] On 18 March 2021, after an investigation into the handling of accusations of sexual abuse on the part of priests in the Archdiocese of Cologne criticized Heße, he announced he was submitting his resignation to Pope Francis.

Heße commended Pope Francis' second encyclical, Laudato si'', which contains the pontiff's strong criticism for consumerism and irresponsible development and his lament for environmental degradation and global warming.

[11] The funding was spent on 90 projects in 70 locations in the archdiocese, with efforts including the improvement of heating systems and insulation, and a shift to green electricity in parishes.

The archbishop admitted that it was not satisfactory that only 25 out of around 80 parishes in the Archdiocese of Hamburg relied solely on green energy.

On 1 August 2015, Heße called for the Catholic Church to be more realistic in regard to teachings on sexual morality.

[14]In a May 2015 interview, Heße spoke about his views regarding marriage and families: "I believe that freedom does not consist of me leaving everything open and free and undetermined, but instead, that I choose and commit myself.

[15][16]On 1 August 2015, Heße announced that he wishes for remarried divorcees "livable forms for the Church's recognition and accompaniment," without giving up the ideal of marriage.

[16]When asked if celibacy was a relief for him, he said:Yes, because I believe freedom does not consist of me leaving everything open and free and undetermined, but instead that I choose and commit myself.

[15][16]In a May 2015 interview, Heße said that he thinks Pope Francis is a "fascinating person, pioneering the way for the Church and today's world.

On 1 August 2015, Heße defended recent reform of the Catholic Church's Labor Law, and critiqued the position taken by some Bavarian bishops who have not fully implemented it, stating:Otherwise, we could not keep going, because we could not find enough qualified employees, in order to be able to run our institutions.

[17] Heße is a fan of organ and classical music, and likes to attend concerts in the Laeiszhalle and the Elbe Philharmonic Hall.