Can I get a temporary/pay-as-you-go EC card for use in Germany?

The EC cards where rebranded as Girocard a few years back and is only available with a bank account.

There are some banks that let (almost) anyone open an account that can only carry a positive balance (as long as you aren't a US citizen or resident). That would take a week or two until you have the card. Usually banks with walk-in branches don't offer free accounts in your situation and online-based banks usually don't have an English-language website.

Any of the free bank accounts at online banks do the trick if you have a German address (e.g. DKB, DAB bank, Consorsbank, comdirect, ING Diba). Opening an account is not too complicated, you fill in a simple online form with your details, print the application, go to a post office with your passport and registration confirmation, and wait for your card. Money to such accounts can usually only be transferred for free with a bank transfer from another european Euro account. All other methods incur a hefty fee. However, comdirect customers can use Commerzbank ATMs to deposit cash for free and 1822direkt customers can use ATMs of the Frankfurter Sparkasse as well.

Maybe a V Pay or Maestro prepaid card would work at that machine but I know no German bank that offers one of those. There are some banks in other countries that have such cards.

I am familiar with the problem: in many places I too have found that only an EC card is accepted by the vendor's card-machine, or by the shop, petrol station etc. I have spent much time researching this. I have been unable to find any bank or institution in the UK which provides an EC card. It appears that one can acquire an EC card only by opening a bank account in a German town or village. To do so may be difficult or even impossible if one is merely on holiday in Germany for a short while, however I think that I will visit a bank in Germany and ask when I am next there. Sorry to have no easy answer. It would be nice to get a clear and official answer from a banking expert. None of the bank staff at my bank in the UK knew anything about this issue and could give me no help. Without an EC card one has to carry sufficient cash in various areas of Germany or else big trouble if you run out of petrol and if the petrol station will not accept any other card.

I think that you could use a "GeldKarte". You should ask your canteen. In the canteen of my university we can only use a GeldKarte, which is implemented on my university ID. It gets very popular around here in the last few years and is a more or less anonymous way for fast money transfer.

The terminal where you have to pay has have this symbol:
_{(source: wikimedia.org)}

You can order it online but should in advance check if you can upload money to it (we have an terminal in our canteen). For the GeldKarte you don't have to have a bank account. You can upload money (up to 200€) on several ways (having a bank account probably by a terminal of your bank, online via card reader, GeldKarte terminals and probably somewhere for cash).