There is no purgatory in Islam; however, hell is probably not going to be eternal. We are expiated for some of our sins by all our suffering in this life, if we're believers.
Indeed hell will not be eternal for any muslim that enters it, but if you meant by that that it wont be eternal for desbelievers iether, then that is a bit alarming for the following reason:
(1) matters about Islam that everyone knows, which even a child raised among Muslims would know, technically termed
ma‘lum min al-din bi d-darura or “necessarily known as being of the religion”;
(2) matters that not everyone knows;
(3) and matters that are disagreed upon even by “those who know,” the
ulema or scholars.
Affirmation or denial of tenets of faith within each category vary in their eternal consequences because of their relative accessibility, and the individual’s opportunities to find them out.
Things That Everyone Knows
To deny anything of the first category above constitutes plain and open unbelief. It includes such things as denying the oneness of Allah, the attributes of prophethood, that prophetic messengerhood has ended with Muhammad (Allah bless him and give him peace); the resurrection of the dead; the Final Judgement; the recompense; the everlastingness of paradise and hell ...
[see 'iman kufr and takfir' by shaykh Nuh keller]