Heinrich Thyssen, after studying chemistry in Berlin, Bonn and Heidelberg, and living for some years in London, where he possibly sought to enter the diplomatic career, settled in Hungary in 1905.

He bought more old masters, from Duccio to Francisco Goya; and fifteen years after his father's death, he bought his first piece of modern art, a watercolor painting by Emil Nolde dated from between 1931 and 1935, starting the entry of 20th century's paintings in the collection (including Pablo Picasso, Piet Mondrian, Edward Hopper, Jackson Pollock, Francis Bacon and Lucian Freud).

However, a settlement was reached between the parties before the baron's death, which brought to a "peaceable" conclusion the wrangling over control of the vast Thyssen art collection, which is to remain in Spain, Hans Heinrich having been the founder of the Thyssen-Bornemisza Museum in Madrid.

One of the paintings in the museum, Rue Saint-Honoré in the Afternoon, Effect of Rain by Camille Pissarro, belonged to a Jewish couple who were forced to give it to the German government in exchange for an exit visa to the United Kingdom shortly after Kristallnacht in 1939.

He married for the third time at Lugano-Castagnola on 17 September 1956 New Zealand-born British photographic and fashion model Fiona Frances Elaine Campbell-Walter (b. Takapuna, New Zealand, 25 June 1932).

They had no children, but Hans Heinrich adopted her son, Alejandro Borja (born Madrid, 1980, son of Manuel Segura), who married at Barcelona, 11 October 2007 Blanca María Cuesta Unkhoff[4] and had two children: Sacha Thyssen-Bornemisza de Kászon on 31 January 2008 and Eric Thyssen-Bornemisza de Kászon on 5 August 2010.