In high spike situations, Google App Engine would anticipate traffic(due to spike) and makes a few instance ready for you. The exact configuration for spinning up and winding down would be based on your appengine-web.xml configuration file(for Java). You may take a look at “Managing App Resources” documentation for a general overview on how to control the idling instances.
The general DeadLineExceededError can have many causes. There is a likelihood that a new instance loading is too slow to handle the requests. Hence, warmup request would resolve the issue.