The electricity supply powers their air-conditioning and fridges.
It also keeps petrol pumps flowing and loads of people are angry that they can't get fuel for their cars.
Up to 2,000 protesters have taken to the streets.
The troops have fired warning shots to try to calm the people down.
'Tempers boiling over'
Now they're providing fuel in tankers to try to ease the petrol crisis.
"The heat, lack of air conditioning and rising temperatures mean tempers are boiling over," said a spokeswoman for the British troops.
There are still around 10,500 British troops based around Basra.
Some people think the power cuts might have been caused by supporters of former Iraqi leader Saddam Hussein, to put pressure on the troops.