How prominent was "prosperity theology" in the early church? Prosperity theology, or the "health and wealth gospel," is a recent movement that teaches that God promises material blessings, in this life, to those who have faith in him and who do his will.  Wikipedia traces its origin to the 19th century, but while researching the subject, I found Augustine apparently addressing something similar in a sermon on shepherding:


  But what sort of shepherds are they who for fear of giving offence not only fail to prepare the sheep for the temptations that threaten, but even promise them worldly happiness? God himself made no such promise to this world. [...]
  
  For the Apostle says: All who desire to live a holy life in Christ will suffer persecution. [...] You say instead: “If you live a holy life in Christ, all good things will be yours in abundance." (LotH, 1010)


This looks like indirect evidence that even around the year 400, Augustine was dealing with teachings similar to those of today's prosperity theology.  Thus I'd like to know:


Is there any surviving direct evidence of these sorts of teachings in the early church?


I.e., surviving writings that actually teach this, as opposed to secondhand accounts

How much indirect evidence is there?
Can we tell how popular these teachings were, and when they gained traction?


I am interested in material after the apostolic age, up to the end of Augustine's life (AD 430).  I know it's somewhat anachronistic to apply the term "prosperity theology" to writings 1500 years older than the movement by that name, but to help clarify what I'm looking for, here's an example, followed by two counter-examples:


God promises1 material2 blessings, in this life,3 to those who have faith in him and live holy lives


This is an example of what I'm looking for; note the three marked elements

God promises blessings to those who have faith in him


Not an example; blessings may be spiritual or material and may not be in this life

God [generally] blesses those who live holy lives 


Not an example; this is a proverb, not a promise
Your question is interesting and it is something that I have talked about a lot Since I was part of that movement in the early 90s and left it only to eventually begin studying Early Church history and theology later.    It is very difficult (possibly impossible) to find anything like the Faith and Prosperity Movement in the Early Church.    While the Early Church did believe in miracles and the supernatural, they had a much different attitude when it came to the lifestyle and compensation of ministers.    Here are a few examples and points to support my thesis.

1A) In 1 Corinthians 9: 1-14, saint Paul argues for the right of apostles and other preachers of the Gospel to make a basic living off of preaching the Gospel (They should have their basic needs met, they should be able to support a spouse to travel with them).    1 Cor 9: 7 Who serves as a soldier at his own expense? Who plants a vineyard and does not eat its grapes? Who tends a flock and does not drink the milk?

1B) Prosperity Preachers take a stronger stance.  They tend to cite the fact that there are wealthy believers in the Bible, people like Abraham and point to the notion that “God wants to bless you” and that “It is possible to be spiritual and wealthy”.

Frederick K.C. Price
“Christ has redeemed us from the curse of the Law, that the blessing of Abraham might come upon us. . . .How did God bless Abraham? With cattle, gold, manservants, maidservants, camels, and asses. Abraham was blessed materially.”13

2A) The Early Church believed in the positive role of suffering.   

2 Corinthians 12:7-10 New King James Version (NKJV)

7 And lest I should be exalted above measure by the abundance of the revelations, a thorn in the flesh was given to me, a messenger of Satan to buffet me, lest I be exalted above measure. 8 Concerning this thing I pleaded with the Lord three times that it might depart from me. 9 And He said to me, “My grace is sufficient for you, for My strength is made perfect in weakness.” Therefore most gladly I will rather boast in my infirmities, that the power of Christ may rest upon me. 10 Therefore I take pleasure in infirmities, in reproaches, in needs, in persecutions, in distresses, for Christ’s sake. For when I am weak, then I am strong.

Colossians 1:24 ►
 Now I rejoice in what I am suffering for you, and I fill up in my flesh what is still lacking in regard to Christ's afflictions, for the sake of his body, which is the church.

2B) Word of Faith and Prosperity teachers frequently preach on God’s willingness to bless, heal and take us away from the trials and suffering inflicted by Satan and his minions.

3)  The Didache also provides concrete evidence that Early church position regarding ministerial compensation was at odds with the Faith and Prosperity movement.   Besides that it also provides evidence against using revelatory “Words” to motivate offerings (as is often done by such preachers).

Didache, Chapter 11
“…Let every apostle who comes to you be received as the Lord. But he shall not remain more than one day; or two days, if there's a need. But if he remains three days, he is a false prophet. And when the apostle goes away, let him take nothing but bread until he lodges. If he asks for money, he is a false prophet.”
“….And every prophet, proved true, working unto the mystery of the Church in the world, yet not teaching others to do what he himself does, shall not be judged among you, for with God he has his judgment; for so did also the ancient prophets. But whoever says in the Spirit, Give me money, or something else, you shall not listen to him. But if he tells you to give for others' sake who are in need, let no one judge him.”