Why is my child limping out of the blue, with no other symptoms; limps without sign of pain?

Several causes. Often young children slide or jump from a height and land on their extended heal & leg rather than flexed leg & their feet. This can put significant pressure on the hip joint & lead to temporary fluid build up in the hip joint. That fluid will cause pain & transient limping which resolves over a day or so. Incidental trauma to the leg, slow moving infection, etc can also cause limp. Dr eval needed.