No nikah al-mut'a isn't punishable (meaning via hadd) in any sunni madhab according almost all sunni scholars and schools (hanafi, maliki and hanbali and the most soundest view of shafi'i jurisprudence school). This can be read in the al-Mawsu'a al-fiqhiya (see for example What is al-Mawsoo’ah al-Fiqhiyyah?):
جاء في الموسوعة الفقهية الكويتية (41 / 342) " ذهب جمهور الفقهاء - الحنفية والحنابلة والمالكية على المذهب والشافعية على الصحيح - : إلى أنه لا حد على من تعاطى نكاح المتعة ، سواء كان ذلك بالنسبة للرجل أو المرأة ، لأن الحدود تدرأ بالشبهات ، والشبهة هنا هي شبهة الخلاف ، بل يعزر إن كان عالما بالتحريم ، لارتكابه معصية لا حد فيها ولا كفارة . ومقابل الصحيح عند الشافعية ، وقول ضعيف عند المالكية : أنه يجب الحد على الواطئ والموطوءة في نكاح المتعة ، لأنه ثبت نسخه " انتهى .
My own translation of the text (take it with the necessary care and feel free to re-phrase it)
In Volume 41/342 the Encyclopedia of Fiqh of the Kuwaiti Ministry of Endowments and Religious Affairs it is said: The majority (jumhoor) of scholars - hanafi, hanbali, maliki school in the (declared) opinion of the madhab and shafi'i according the strongest (most sane) opinion- say: there's no punishment (hadd حد) for those who perform mut'a marriage نكاح المتعة, no matter if it is for a male or female, because punishment(hudud حدود) are driven off in case of suspicion (no penalty on suspicion criterion). Here the suspicion is the one of differences (khilaf خلاف) in opinions among Muslims.
If somebody performs it knowing it is (considered as) haram than t'azeer تعزير would be applied on him.
The other view of the shafi'i school and a weak opinion of the maliki school however says that hadd punishment must be applied on both parties (the male who penetrates the woman's vagina and the woman whom has been penetrated this way) in case of muta' marriage, because the abrogation is affirmed" End of the quote taken from islamqa #216785
From wikipedia on Ta'zeer:
In Tazir cases, the punishment is at the discretion of the state, the ruler, or a qadi (kadi), or court acting on behalf of the ruler.Tazir punishment is for actions which are considered sinful in Islam, undermine the Muslim community, or a threaten public order during Islamic rule, but those that are not punishable as hadd or qisas crimes. The legal restrictions on the exercise of that power are not specified in the Quran or the Hadiths, and vary. Crimes punished by tazir do not require proof that hadd or qisas crimes require, such as four male Muslim witnesses. The judge enjoys considerable leeway in deciding an appropriate form of punishment, and the punishment does not have to be consistent across the accused persons or over time. The ruler or qadi also has the discretion to forgive tazir offenses.
As already mentioned in my earlier comment, in his sahih al-Bukhari referred a statement considering nikah al-mut'a as valid (in case of trickery) to some student of abu Hanifa, also see What does it mean by the marriage is valid but its condition is illegal ? [hadith explanation]!
