...Does a "loving god" burn his children ?
The reason "purgatory "is a mystery is because it is not anywhere found in the teachings of Christ or His apostles..
A loving God did not choose for us to sin, but He does choose to forgive. That forgiveness following our deaths is called Purgatory by the Catholics, Anglicans, High Church and Lutherans. Even John Wesley, the founder of Methodism, believed in an intermediate state between death and the final judgment and in the possibility of "continuing to grow in holiness there.
What is called apocatastasis by St. Peter in Acts, the third heaven by St. Paul in 2 Corinthians, and Gehenna in Zechariah 13 is Purgatory.
Peace be with you.