From the many lies against Ibn Taymiyyah is that he does not believe in the eternity of the Hellfire. The reason for this doubt is that his student Ibn al-Qayyim (rahimahullaah) inclined towards this view, outlining it's evidences, and showing the strength of this position, without actually indicating explicitly that he holds it out of firm conviction. When he mentioned the evidences for this view in his books such as Haadi al-Arwaah,and Shifaa al-Aleel, he made reference to the fact that Ibn Taymiyyah has mentioned a number of views regarding the matter, from which was the saying that the Hellfire is not eternal and will expire. However, the innovators took this to mean that Ibn Taymiyyah actually held this view, when in reality, Ibn Taymiyyah simply mentioned the views of various factions, and then proceeded to refute what is incorrect and establish what agrees with the Book and the Sunnah as is his habit. As for Ibn al-Qayyim, upon study of this subject in his numerous books it appears that he was not committed fully to the view, but considered the arguments for it to be very strong and inclined towards it. One can find him expressing another second opinion as occurs in his other books such al-Waabil al-Sayyib and Tariq al-Hijratayn, which is that Hellfire is eternal (the correct view). In any case, Ibn al-Qayyim supported the view of Hellfire not being eternal and coming to an end partially because of the presence of narrations from the Companions that indicate this, and he was not the first to express this view, with our knowledge that his writings only indicate his belief in the strength of argument for this view, not that he wholeheartedly believed it to be actually true.

One should note that Ibn al-Qayyim's position in the first of his two views has no connection with the doctrine of the Jahmiyyah regarding the expiration of Paradise and Hellfire. Since the origin of the saying of al-Jahm bin Safwaan in this regard is based upon the principle of "the impossibility of an endless chain of events" in both the past and the future and "whatever is not devoid of hawaadith is itself haadith (originated)". Upon this, the Jahmiyyah denied Allaah's chosen actions, and this led them to many corrupt statements in belief, including the statemennt of the Qur'an being created and the claim of the non-eternity of Paradise and Hellfire. As for the view that Ibn al-Qayyim tended to, then the origin of that is either a general text (in the Qur'an) or narrations (from numerous Companions) that are not authentic. Hence, Ibn al-Qayyim (in the first view he inclined towards) simply spoke with a view that is marjooh, daeef (weak) as Imaam Ibn Baz explained (see here) and his position has nothing to do with the Jahmiyyah. Far from it. On the contrary, Ibn al-Qayyim demolished the particular foundation of the Jahmiyyah upon which their corrupt doctrines are built. For more information and elaboration, please refer to the articles (here)(here) and (here).