How do I extinguish a burning colonist?

I had an explosion in my battery bunker, and when my people arrived to clear the fire, 7 out of 9 caught fire and burned to death.

How can I put out the fire on my people when it is not raining?

I had an explosion in my battery bunker, and when my people arrived to clear the fire, 7 out of 9 caught fire and burned to death.

Was the fire completely inside then? Or did it blow out part of the walls?

If a fire is within a room that sealed off from the outdoors, temperature becomes a huge problem. The temperature in the room will quickly climb into the hundreds of degrees, anyone that ventures into the room to try and put out the fire will not be able to stay safely in the room for very long without having problems with the heat/catching fire.

Usually when a colonist catches fire, they're fairly competent at putting themselves out as long as they're not trapped in a corner or have their movement impaired by something else.

As soon as someone catches fire, they start panicking and I'm going to assume (from what I've seen at least) their movements whilst on fire are pretty random. So it sounds like your people moved into an indoor room to try and put out a fire, caught fire to due the insane temperature and then couldn't put themselves out because the temperature was too high, and couldn't move outside to a safer temperature due to their random movements whilst being on fire, so they quickly died.

If this was the case, and you do have a fire "indoors", a safe way to deal with it is to mark some building's wall for deconstruction before you start trying to handle the fire. As soon as the wall's deconstructed, the room is no longer classified as "indoors", as there's a massive gap allowing the temperature to stay at much safer levels, which will now let your colonists safely tackle the fire.

This becomes slightly more difficult if a fire breaks out deep into the tunnels of a mountain settlement, as you can't as easily create holes to let the heat out, and when it's happened to me I've had to completely evacuate and just watch everything burn rather than risk sending people in to try and put it out.

Once a colonist is on fire, they will put the fire out themselves or the fire will be extinguished by the rain. There's not much you can do.

However, you can prevent them from being on fire in the first place. Make sure they're never surrounded by fire, and if they look like they will be, draft them and move the colonist a safe distance from the fire. Make sure that colonists are fighting the fire at the edge, not the center. Finally, if they're in a small room with a fire, don't let them fight fires unless you are sure that you have enough colonists to extinguish faster than it will spread so that no one will become trapped.