The pile can catch fire if there is no moisture, and the heat can drive off a lot of moisture too (the steam you saw). If the material is not moist, sprinkle it with the hose. It takes quite a lot of water to soak all the way down into it. If you are moving the pile, you can add a little water as you go, spraying it each time you add 6 inches worth. I live in a very dry climate and I have to water all my compost, what little I do any more. Mostly I just spread it out as mulch beds and that does not heat up or catch fire. But for piles, I run an oscillating sprinkler, the kind that tap tap tap around, one hour for every foot thick. Then I check how far down the water has penetrated and run more as needed.

Any pile of organic matter will spontaneously combust, catch fire, if all the conditions necessary are present and one of these is moisture. Your pile of wood chips had enough Nitrogen (wood chips, especially young wood) can have very high levels of Nitrogen, enough moisture, and sufficient air for bacterial activity to quickly take place and that is what caused the rise in temperature in your pile, bacterial activity.
Once you have that material spread out, with less volume, the whole digestion process will slow down and not generate so much heat.

It can happen but is not likely in my experience. I have had bigger very hot piles that did not combust. The high temperature normally dissipates within a few days. You can spread it out, dig out a vent hole in the center or a vent trench bisecting the pile or otherwise dissipate the heat if you are worried. If it's extremely hot you will have to spread it out from the edges as it will be too hot to comfortably stand on. The arborist I use says that crews have been known to use hot wood chip piles to warm up on when they are working outdoors in the winter.

Thanks so much ya'll......I went ahead and spread the rest of the pile out just to be safe. That's funny Bob about the crew standing on the pile to stay warm. Thanks again for great advice.

I got a few loads of wood chips this past year and they did heat up a lot. They usually cooled off after a while and nothing went up in flames here but we are not in a drought here this season.

I've run out of my chip piles though and I need to get them to bring me another load.

Here is a link that might be useful: my bins

Here's my 2 cents; don't spread that pile out. I am highly doubtful that it will burst into flames and since wood chips take so long to decompose, I would do everything in my power to keep it hot and decomposing.