A heart for children is:

… a heart where God resides and rules.

Isa 57:15

For thus says the high and lofty One who inhabits eternity, whose name is Holy: I dwell in the high and holy place, and also with those who are contrite and humble in spirit, to revive the spirit of the humble and to revive the heart of the contrite.

… a heart that is contrite and humble.

Matt 25:34-40

"Then the King will say to those on his right, 'Come, you who are blessed by my Father; take your inheritance, the kingdom prepared for you since the creation of the world. For I was hungry and you gave me something to eat, I was thirsty and you gave me something to drink, I was a stranger and you invited me in, I needed clothes and you clothed me, I was sick and you looked after me, I was in prison and you came to visit me.'

"Then the righteous will answer him, 'Lord, when did we see you hungry and feed you, or thirsty and give you something to drink? When did we see you a stranger and invite you in, or needing clothes and clothe you? When did we see you sick or in prison and go to visit you?'

"The King will reply, 'I tell you the truth, whatever you did for one of the least of these brothers of mine, you did for me.'

… a heart that understands what really matters.

If I could speak in any language in heaven or on earth but didn’t love others, I would only be making meaningless noise like a gong or cymbal. If I had the gifts of prophecy, and I knew all the mysteries of the future and knew everything about everything, but didn’t love others what good would I be? And if I had the gift of faith so that I could speak to a mountain and make it move, without love I would be no good to anyone. If I gave everything I have to the poor and even sacrificed my body, I could boast about it but if I didn’t love others, I would be of no value whatsoever. 1 Cor. 13:1-3 NLT

… the heart of a child.

Mark 10:14-15

When Jesus saw this, he was indignant. He said to them, "Let the little children come to me, and do not hinder them, for the kingdom of God belongs to such as these. I tell you the truth, anyone who will not receive the kingdom of God like a little child will never enter it."

To have a heart for children we must have the heart of a child.

Story from Landon Saunders:

When ever the new Harry Potter books come out kids are asked to write essays about some feature of the book.  Recently they were asked to write about “If you had the magic wand, what would you do?”. One little boy wrote:

If I had the magic wand I would go throughout the entire world and heal the broken hearted because I have looked around and there are lots of broken hearts and no one seems to know what to do. I know about broken hearts, he said, because my heart is broken. My mother dies two years ago and my heart is still broken. So if I had the magic wand what I would do is I would go heal broken hearts.