I’m less inclined today to search my own heart, but rather ask God to do so. I find that when I search my heart I find more than I can handle, (some of it true, some of it not) but when I invite God to do so, he carries the burden for me. My former inclination to heavy introspection is made to be seen as the exhausting chore that it is. There is a difference between “examining yourselves” and searching your hearts (see end of post, but for now).
When I search the Scriptures I also see the teaching tells me to do this: to ask God to search my heart. It seems out of place to take the role that the Psalmist and others invite only God to do. Moroever in the few examples of man searching his own heart it is not entirely positive at all. Introspection appears to be a novel lie and disappointment. We need God to search our hearts. Examples below:
Psa. 139:23 Search me, O God, and know my heart!
Try me and know my thoughts!
Eccl. 1:13 And I applied my heart to seek and to search out by wisdom all that is done under heaven. It is an unhappy business that God has given to the children of man to be busy with.
Eccl. 2:3 I searched with my heart how to cheer my body with wine—my heart still guiding me with wisdom—and how to lay hold on folly, till I might see what was good for the children of man to do under heaven during the few days of their life.
Eccl. 7:25 I turned my heart to know and to search out and to seek wisdom and the scheme of things, and to know the wickedness of folly and the foolishness that is madness.
Jer. 17:10 “I the LORD search the heart
and test the mind,
to give every man according to his ways,
according to the fruit of his deeds.”
Zeph. 1:12 At that time I will search Jerusalem with lamps,
and I will punish the men
who are complacent,
those who say in their hearts,
‘The LORD will not do good,
nor will he do ill.’
Rom. 8:27 And he who searches hearts knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God.
Rev. 2:23 and I will strike her children dead. And all the churches will know that I am he who searches mind and heart, and I will give to each of you according to your works.
Examining yourself to see if you are of the faith has to be something different than searching the heart. It likely deals with looking at real evidences for gospel transformation in your lives. The text is 2 Corinthians 13:5.

2Cor. 13:5   Examine yourselves, to see whether you are in the faith. Test yourselves. Or do you not realize this about yourselves, that Jesus Christ is in you?—unless indeed you fail to meet the test!

The problem was that instead of examining themselves for gospel fruit, they were scrutinizing the apostle Paul. Paul turns the table and calls them to see if they have gospel fruit in their lives. That is not introspective searching of the hearts, that is looking to see if you have a transformed life externally based on an inward belief and public profession.

We should then see that introspection is different than examination. The former is often taken to be godly, but really is not. When we want to know our hearts, we really need to ask and invite God to search us. When we are looking to examine our lives, we should do so as to not live lies and betray the faith. The two are very different things. Beware of the danger of introspection, and pursue the examination of gospel fruit in your lives and in the lives of those you admit as members of the church.