How can the continual burnt offering be taken away if there is no Temple? 

First of all, neither Daniel 11:31 nor 12:11 mention burnt offering, or sacrifice, as is meant throughout the O.T. In the Hebrew we read only HaTamid, which translated means the continual, the perpetual, the constant, the regular, the always, [the daily]. Naturally, this may refer to the daily sacrifice, as has been assumed. But except for Daniel 9:27, the Spirit leaves the mention of olat tamid [burnt offering, sacrificed twice daily], or of mincha [daily meal offering made in the morning and afternoon], or of zevach/zavach [slaughterd sacrifice] out. I.e., something which is not necessarily a burnt animal sacrifice is offered up to G-d there daily, and this type of continual offering will be made to cease.

There has been a HaTamid/continual [sacrifice], apart from the Temple, since the days of the Babylonian captivity. This continual has not ceased and its practice can be observed in our days at the Western Wall (the Kotel) of the Second Temple in Jerusalem. What is it? It is the prayers of Israel at the time of the morning  and evening sacrifices, and at the hour of the burning of incense, at 3:00 p.m.²⁷. Daniel prayed three times a day, precisely at the hours when the daily oblations were to be offered in the Temple. Ever since the destruction of the Second Temple and the Great Dispersion religious Jews have practiced Daniel’s continual mincha [morning and evening prayer services], even as it is written: 

“Sacrifice and offering you do not desire, but you have given me an open ear. Burnt offering and sin offering you have not required... I delight to do your will, O my G-d; your law is within my heart .”  And, “I will offer to thee the sacrifice of thanksgiving and call on the Name of the L-RD;” and “Let my prayer be counted as incense before thee, and the lifting up of my hands as an evening sacrifice.”²⁸

When the children of Ishmael threw rocks from the grounds of the Dome of the Rock upon the children of Isaac worshiping at the Western Wall [Kotel] beneath, this HaTamid was interrupted until order was restored. And at the latter time of the end the natural firstborn of Abraham, Ishmael, will appear to triumph over the spiritual firstborn of Abraham, Isaac, as well as the natural firstborn of Isaac, Esau, over the divinely elected firstborn, Jacob. To this the Dome of the Rock bears visible testimony as it still towers above the humble remains of the Jewish Temple.

And the day will come when no Jew nor ingrafted Gentile will be able to offer up his/her morning and evening sacrifices of prayer and praise at the Wailing Wall! The beloved Kotel, where the hearts of the children of Israel beat as one, and where G-d’s eyes and heart abide²⁹, will stand bereft of the continual sacrifices of prayer [mincha services], because the “fortified” sanctuary of Islam on the Temple Mount will claim her as part of her dominionZ. A UN contingent (as already requested by Yasser Arafat) and PA militia will eventually patrol the Western Wall Plaza, not allowing any non-Muslims to approach or pray at the wall. Eventually the sacriligious thing, which will lead to the desolation of the whole earth, will be set up³⁰, apparently within the confines of the abomination already standing in the Holy Place³¹.

The thing that shall be set up is thought by many to be some idol, or statue. However, neither of these things would have the power to desolate the earth. But today’s generation of men is indeed already in possession of weapons capable of devestating the earth. The ultimate weapon for which the leading powers of the earth are in a desperate race is the untraceable, indestructable --- computer virus! Invading a nation’s computer system with a virus that will both paralyze every aspect of national life and incapacitate that nation’s defense system, is today’s fierce “arms’ race”. The consequences of such a total “paralysis” would be catastrophic. The aggressor could destroy without having to face a powerful counter attack, if the nation under attack is unable to neutralize both the paralyzing and crippling virus, as well as the “misinforming” one. 

The Hebrew of the verses 38 and 39 of Daniel 11, read with the the  in mind, shows a man devoted totally to the concept of force, who literally “worships” military might (although he may maintain an outward form of traditional religion). It is his “god”, and on this god he lavishes every treasure he can lay his hands on. From this Scripture it appears that eventually he will obtain the ultimate of electronic warfare equipment, something so advanced and powerful that he can cripple, and overcome any counter force. His fortified sanctuary impenetrable, the force of his “god” unstoppable, he will magnify himself above all, as he realizes that none can overthrow his “god”, his sanctuary, nor him. Esteeming himself all-powerful in view of the most powerful nations’ inability to penetrate his force and defense, he will break the agreement he made with many cosigners, and speedily spread his abominable reign of terror across the globe with fearful destruction in its wake. It may be that, because he controls the very Mount upon which the Jews await their G-d’s Return, he thinks himself invincible³². Being so utterly persuaded of his invincibility, he will array his forces to fight even against Messiah Yeshua at His Return. But at that time the desolator shall meet his Master, when the King of Israel, the Judge of all the earth, shall slay him with the sword of His mouth³³. 

Even then, no Jewish Temple crowns the Temple Mount.