Thanks everyone for your advice.
What I've been doing so far is using boiled water from the kettle. I'm staying with my parents, who drink tea like nobody's business. So the kettle water hardly ever goes cold. It's left more than half an hour though. And in the night it's quite cool.
I tried putting the water in the fridge but it seemed to take longer to warm the water up than it did to cool the water down! And she's only really drinking 60mls now, so it's a bit tricky to half-fill bottles, although I think that's a good idea for when she's a bit bigger.
So far so good. Although my Dad seems to have an uncanny ability to boil the jug about three seconds before the baby cries. Luckily she's doesn't really get worked up and is happy to suck on a finger for a little while, just making small complaints about the service.