I am a Premillennialist scholar, believing Christ will reign for 1000 years on earth, but I believe there is significant biblical evidence that there won't be animal sacrifices nor a temple in the Millennial Kingdom.
He says that sacrifices will be made as an object lesson in memory of past sins, but there's no verse to support this. Hebrews 10:3 is talking about those in the Old Covenant, based on Hebrews 10:1. Animal sacrifices were made under the Old Covenant as atonement for sins (Leviticus 17:11), but this system was made obsolete (Hebrews 8:13) because it cannot take away sin from the conscience (Hebrews 10:11).
Purified Conscience Negates Lessons
Because Jesus' sacrifice purifies our conscience (Hebrews 9:14), sacrifices have ceased forever:
Otherwise, would they not have ceased to be offered, since the worshipers, having once been cleansed, would no longer have any consciousness of sins? (Hebrews 10:2)
Where there is forgiveness of these, there is no longer any offering for sin. (Hebrews 10:18)
He says there'll be a need to teach sinners how offensive sin is, but the reason offerings have already ceased is that now God's laws are already written on the believer's heart (Hebrews 10:16), so much so that the memory of our sin in Christ's mind is put away:
then he adds, “I will remember their sins and their lawless deeds no more.” (Hebrews 10:17
In short, there is no need for an object lesson of the pains of sin when our purified conscience that has God's laws written on it causes God to remember our sins no more. Paul was saying in Hebrews 10:3 that being reminded of sin yearly is a necessary evil, proven in verse 17.
Ezekiel is not Prophecying the Millennial Kingdom
Ezekiel can't be prophesying the Millennial Kingdom for many reasons, most importantly:
And I saw no temple in the city, for its temple is the Lord God the Almighty and the Lamb. (Revelation 21:22)
- John said that there is no temple in New Jerusalem because Jesus is the Temple (Revelation 21:22), and the same applies to Jesus reigning in the 1000 years.
- Only those circumcised in flesh may enter the sanctuary (Ezekiel 44:9), but Paul tells us to not circumcise ourselves anymore (I Corinthians 7:18).
- Offerings are for God's acceptance (Ezekiel 43:27), but Christ accepts the faithful (Romans 5:1).
- Only the "prince" may eat with the Lord Jesus (Ezekiel 44:3), yet in the Marriage Supper of the Lamb, everyone eats with Him (Revelation 19:9) and fortunately, everyone sees His face (I Corinthians 13:12).
Ezekiel is Prophecying the Third Temple
Ezekiel's Temple has been controversial. His prophecy happened after Solomon's Temple (The First Temple) was destroyed. Some think it was Zerubbabel's Temple or Herod's Temple (The Second Temple), but the dimensions and designs are too different. I mentioned earlier how it can't be the Millennial Kingdom's temple.
This leaves room for one more temple: the Third Temple. Jews have been trying to build it recently, but it's difficult because the Muslim's Dome of the Rock is there. Before the Antichrist comes, the Jews will have succeeded in building Ezekiel's Temple (II Thessalonians 2:4; Revelation 11:1). This makes sense further because the Jews still adhere to many traditions like circumcision. They don't do animal sacrifices because they don't have a temple, but many Jewish leaders want to go back to animal sacrifices once their Third Temple is built.
Some say that can't be the case because the temple and Jesus will dwell forever (Ezekiel 43:7), but notice the phrase "this is the place" and "will" in the verse. God is saying that New Jerusalem and the Millennial Kingdom will be located at the site of Ezekiel's Temple.
Spirit-led Christians Don't Sacrifice
Although many nowadays have the Holy Spirit, most are not led to sacrifice animals in memory of our sins. It wouldn't be logical for Christ to re-instate this after "doing away" with it (Hebrews 10:9-10).
For these reasons, no more animal sacrifices will be made by Holy Spirit-led Christians after Jesus' resurrection.
When the GotQuestions author says "Most premillennial scholars agree", I believe he means that most people who he talks to. There is no poll about this that I'm aware of.
I also wrote more about heaven if interested at Answering Problems.