The short answer is never.

The long answer is that the Church in the medieval period did not carry out punishments on heretics, but that heretic who were to be punished were handed over to secular authorities (i.e. the local king/count/duke etc.) to be punished. But in the vast majority of cases, this was not a punishment for heresy, but for heretics who had relapsed, who had confessed and been forgiven for their erroneous beliefs, but who later reverted to heresy. The goal in every case of suspected heresy was to get the suspected heretic to renounce the heresy and return to the true faith, thereby saving their immortal soul - this was the standard practice of the Church's inquisition in the south of France in the thirteenth and fourteenth centuries. Even the most famous burnings for heresy of the Middle Ages, that of Jacques de Molay and other Templar leaders in 1314, was not for their many alleged heresies, but for recanting their earlier confessions (Templar brothers who had confessed and repented were allowed to live out their days in other monasteries and religious houses, with heavy penance.)

In fact, the only direct case of burning for heresy without this process of confession and recanting that I know of is the so-called Orléans heresy. This was a small heretical movement which spread among learned circles of Churchmen in central France and was condemned by King Robert II of France at a council in Orléans in 1023 (although, like many medieval heresies, there was almost certainly a political element to these accusations too). It's important to note here that it's Robert, not the church itself, who decided to execute the heretics (between 10 and 14, according to various accounts). Even so, the hope was that the threat of execution would cause the heretics to recant, as the historian Ralph Glaber makes clear:

When many had employed all their ingenuity in seeking to make them [the heretics] abandon their dangerous ideas and accept the true and universal faith, and they had altogether refused, they were told that if they would not rapidly return to a proper notion of the faith, on the king's orders and with the consent of the whole people they should be delivered over to the flames without delay. But they were confident in their evil madness [...]. The king and those with him saw that they could not be recalled from this folly; he ordered that a huge fire should be lit not far from the city; hoping that the sight of this would frighten them into giving up their malign belief.

(Rodulfus Glaber, Histories, Book III, chap. 31, trans. John France)

So execution for heresy was always a last resort, and for the best part of the middle ages was never actually for heresy itself, but for relapsed heretics, and was carried out by the secular government, not by the church itself.

[N.B. This answer is about central and later medieval heresy. The late antique and Early Christian heresies you mentioned in your OP (pelagianism and arianism) were not, AFAIK, punished by death, but I don't really know enough about them to comment.]