K4 and K24 both are equipped with air conditioners. They are of the same type. They both depart from Erlian at 00:57 and arrive in Beijing at 14:04. Their tickets are at the same price. Hard seat: CNY64; Soft seat: CNY107. Hard sleeper: CNY122/126/131; Soft sleeper: CNY193/202.
You'd better go to the railway station to buy the ticket as soon as possible. Usually, railway station sells the ticket three days ahead of the departure date.