UK Income Tax on temp work?

Probably not the best place to post this, since it is a travel board, rather than an overseas employment one. Plus it may depend on your exact circumstances.

However, in general terms if you are on an employed basis (rather than self-employed contractor) then income tax and national insurance contribution is normally handled via your employer (PAYE - Pay As You Earn). If you have a tax liability in another country, particularly if you are a American citizen, then you have to deal with the other appropriate authorities.

The normal rule is that if you are in a country for more than 6 months in a tax year, then you are liable for income tax. But, if you pay UK income tax, you should be exempt from German income tax for that period.
In the UK income tax works as "PAYE" (= Pay as You Earn). The employer deducts tax "at source" and pays you the net amount after tax. The only people who have a bill to pay are self employed.

You will need to open a UK bank account because you will be paid in £ (pounds). If you employer paid your salary to a German Bank account (in €), you would both have bank charges.

I am assuming you are a German citizen and therefore there is no work permit issue, at least until BREXIT next March.

If you are "currently" living in Germany is it possible that you are neither a German citizen nor an EU citizen?

You will more than likely be paid via PAYE, meaning tax will be taken before your salary even gets into your bank so you have nothing to worry about - you can calculate that here: http://salary-calculator.org.uk/ . Personally I would keep the UK bank account in case you end up overpaying in tax, which will be returned at the end of the tax year.