Thank you for your question. There is only one way to find out more about the circumstances surrounding your uncle's passing. That is to apply to access the file of the death in the State Prosecutor's Office in Giessen, Germany. The procedure is called 'Akteneinsicht'. The problem is that they only do it either 1) in person or 2) through a German attorney (there is a special system for the electronic transfer of information to which only German attorneys have access); or 3) through a German-speaking attorney via fax (it has worked before).
The other issue is your entitlement to view the file. If your uncle has any closer relatives that may be interested in answers, it would be best that the request is addressed by them (such as your parents). This is because, for 3rd degree and other relatives, the authorities usually request a court declaration that you have a legal interest to view the file, the court being the local Amtsgericht in Giessen (thus another barrier).
Finally, regarding the death certificate, it can be ordered on-line here: https://www.giessen.de/showobject.phtml?La=1&object=tx%7C684.6121%7C0&ModID=10&FID=640.2963.1 (link). Again, I would suggest someone more closely related to your uncle would be better placed to make the request. Alternatively, it can be obtained in person at the civil status office (details in the same link). The problem is that the cause of death is not written in German death certificates, as per article 60 of the Civil Status Law. Therefore, you would only find information like the place and time of death, but not the cause.
I hope this gives you some useful information. If you really wish to investigate further, especially for such an older case, I would suggest contacting a local attorney who has the time and means to research the State Prosecutor's file in person.
I look forward to any further questions and to your rating.
Dr Ioan-Luca Vlad