According to Mahābhārata, only the man is to be blamed if a woman commits adultery, so any kind of punishment on earth or hell does not apply to the woman:
If men, after accepting the hands of wives in marriage and pledging themselves to earn religious merit without being dissociated from them, seek congress with other people's wives, they then cease to be worthy of respect. The husband, because he supports the wife, is called Bhartri, and, because he protects her, he is on that account called Pati. When these two functions disappear from him, he ceases to be both Bhartri and Pati. Then again woman can commit no fault. It is man only that commits faults. By perpetrating an act of adultery, the man only becomes stained with guilt. It has been said that the husband is the highest object with the wife and the highest deity to her. My mother gave up her sacred person to one that came to her in the form and guise of her husband. Women can commit no fault. It is man who becomes stained with fault. Indeed, in consequence of the natural weakness of the sex as displayed in every act, and their liability to solicitation, women cannot be regarded as offenders. Then again the sinfulness (in this case) is evident of Indra himself who (by acting in the way he did) caused the recollection of the request that had been made to him in days of yore by woman (when a third part of the sin of Brahmanicide of which Indra himself was guilty was cast upon her sex). There is no doubt that my mother is innocent.
Even assuming the woman is at fault, the Manusmṛti prescribes the following punishment.
If a woman, proud of relations and her qualities, passes over her husband, the king shall have her devoured by dogs in a place frequented by many. — (8.371)
Medhātithi's commentary (manubhāṣya):
‘Passing over’ means neglecting the husband and going over to another man; if a woman does this through ‘pride,’—the pride consisting in the idea,—‘I have several relations who are powerful and wealthy, and I myself am possessed of all the excellent qualities of a woman, such as beauty and love,—why then should I mind my character?’
Such women the king shall get devoured, till they die.
The Manu contradicts itself by also prescribing a simple prāyaścitta (atonement) for adultery:
If the wife is particularly corrupt, her husband should keep her confined in one room, and should make her perform that penance which has been prescribed for males in cases of adultery.—(11.176)
If she happens to be corrupted again, on being solicited by a man of equal caste,—then the Kṛcchra and the Cāndrāyaṇa would be the means prescribed for her purification.—(11.177)
Now according to this verse (from Viṣṇu Purāṇa) quoted in this answer, after having undergone a punishment or prāyaścitta for a sin on Earth, a second punishment ("double retribution") in hell doesn't apply:
yāvanto jantavaḥ svarge tāvanto narakaukasaḥ /
pāpakṛd yāti narakaṃ prāyaścittaparāṅmukhaḥ // ViP_2,6.36 //
(And through these stages) the beings that are either in heaven or in hell are destined to proceed, (until final emancipation be obtained.) That sinner goes to Naraka who neglects the due expiation of his guilt.