Solomon is never mentioned very Positively in The New Testament.

Matthew 12:42 and Luke 11:31 are both about Jesus proclaiming himself greater than Solomon.  Of  course the next verse does the same with Jonah, and elsewhere Jesus also refers to Jonah in a sense clearly making him a type of Christ, but there is no equivalent to that for Solomon.

Matthew 6:28-29 and Luke 12:27 are outright dismissive of Solomon’s glory, declaring it inferior to the Lilies of the Field.

Matthew's genealogy of Jesus in chapter 1 verses 6 and 7 mentions Solomon.  But it also mentions Manasseh and Amon and Ahaz, even though Matthew made a point to skip some of the bad kings of Judah, he didn't skip them all.  There is disagreement about if Jeconiah was skipped.  2 Chronicles tells us Manasseh repented, but 2 Kings doesn't mention that.

Three verses that use the name of Solomon are just referencing Solomon's Porch as a location, those include the only time you see it in John, and the other two are in Acts 3 and 5.

Solomon isn't mentioned in Hebrews 11, or by James in his parallel passage.  He's never mentioned by Paul, not even in Acts 13 where he mentions Saul and David.

But the key reference to Solomon in the New Testament I want to draw attention to is Stephen’s in Acts 7:47, in his summary of Israel's history.

Acts 7:44-50

Our fathers had the tabernacle of witness in the wilderness, as he had appointed, speaking unto Moses, that he should make it according to the fashion that he had seen.  Which also our fathers that came after brought in with Joshua into the possession of the Gentiles, whom God drave out before the face of our fathers, unto the days of David; Who found favour before God, and desired to find a tabernacle for the God of Jacob.

But Solomon built him an house.  Howbeit the most High dwelleth not in temples made with hands; as saith the prophet, "Heaven is my throne, and earth is my footstool: what house will ye build me? saith the Lord: or what is the place of my rest? Hath not my hand made all these things?"

According to this, what Solomon did in building his Temple was NOT what David intended.  Why would he say that?  (BTW, the Prophet Stephen was quoting was Isaiah, chapter 66 verses 1 and 2.)

II Samuel 7 is the origin of David's desire to build a House of some type for Yahuah.  And even if he didn't change his mind on that based on what Nathan said, what David wanted to build was a House of Cedar, of Wood.  Cedar Trees were involved in the construction of Solomon's Temple, but it wasn't mainly a Wooden structure, it was a Stone building.  1 Kings 5:18 and 6:7, and 7 :9-12.

Now David mentioned Stone in his instructions to Solomon in 1 Chronicles 22, but it's possible their intended involvement was minimal compared to what Solomon did.  In fact 1 Chronicles 22 account of David preparing much of the material in advance is interesting given how in 1 Kings especially Solomon didn't use those but got his own.

It's possible that Solomon even used the wrong location.  2 Chronicles 3:1 tells us Solomon's Temple was built on Mount Moriah, the threshing floor of Ornan the Jebusite (also called Araunah) that David purchased.  But the earlier accounts of David buying that land in 2 Samuel 24 and 1 Chronicles 21, are not said to be where The Temple would be, just an Altar for a special Sacrifice to atone the Sin of the Census.

Well that's the case with Samuel, without the modern Chapter divisions 1 Chronicles 22 can be assumed to be referring to that same location from 1 Chronicles 21.  But Samuel has no equivalent to 1 Chronicles 22.

Psalm 132 tells us where David found the place for his Tabernacle, Ephratah which is also Zion The City of David.  Most people think the Tabernacle of David was never called a Mishkan, but that's because they're leaving Psalm 132 out of that subject.  The New Testament quotes Davidic Psalms a lot, but never the actual narrative of Samuel, Kings or Chronicles.

I've expressed support before for the Tabernacle being a Dome as some have argued.  In the past I'd felt that maybe that was true of Solomon's Temple also.  Now I'm thinking maybe not, maybe Solomon was influenced by the design of Pagan temples like the one at Ain Dara.

The Hebrew word Dbiyr (Translated Oracle in the KJV) could be a clue to Solomon’s Temple not following the intended design.  It’s never used in The Torah or of The Tabernacle, or in David’s instructions for Solomon in 1 Chronicles 22.  It’s used mainly in descriptions of Solomon’s Temple in 1 Kings and 2 Chronicles, seemingly as a synonym for the Holy of Holies.  It is used in one Davidic Psalm, but that’s poetic language.  The references referring to the Oracle do seemingly make the Holy of Holies a separate room, in contrast to what I observed about The Mosaic Tabernacle in my Vail of the Tabernacle post.

Those are conjectures for why.  Maybe they’re wrong but the point is Stephen said Solomon didn’t do as David intended.

Solomon has been argued to be a type of The Antichrist based on 1 Kings 10:14 and 2 Chronicles 9:13 saying the amount of Gold that came to him in one year was Six Hundred and Sixty Six talents.

My argument that the Second Temple might not have been built over Solomon’s Temple but over part of Solomon’s Royal Palace, could have interesting implications for the Abomination of Desolation.  The Antonia Fortress was also over it in that view, with Solomon’s Judgment Seat possibly being where Pilate’s was.

Now this goes against my own personal biases a bit since one of the books attributed to Solomon, The Song of Songs that is Solomon's, has been important to arguments I've made on my Sola Scriptura Christian Liberty Blog.  However The Holy Spirit spoke genuine Prophecies through the mouth of Balaam, and even Caiaphas in John 11:49-52.  So this negative painting of Solomon need not require rejecting the Canonicity of the Scriptures that Solomon wrote.  2 Peter 2:22 does quote Proverbs 26:11, and Romans 12:20 quotes Proverbs 25:21-22, and Hebrews 12:5-6 quotes Proverbs 3:11-21.

Update March 20th 2018: I've posted a follow up of sorts here.