Are there any precepts among those of the Decalogue that have reference to the parts of temperance?
No, there is no precept which refers directly to the parts of temperance, because these of themselves do not refer to man's dealings with God or his neighbour. Nevertheless these divers parts are referred to indirectly by reason of their effects, and this either by the precepts of the first table or by those of the second table. It is for instance through pride that man does not give to God or his neighbour the respect due to them; and it is through anger that man assails the person of his neighbour even to the attempting of his life (CLXX. 2).
Would it not have been fitting to speak in the Decalogue of the positive side of the precepts that relate to temperance and its parts?
No, because the Decalogue should contain only the first precepts of the divine law such as are applicable to all men and to all times; but whatever belongs to the positive side of these virtues, as abstinence, the manner of speaking, acting, etc., can vary with different peoples, in different places, in different times, etc. (CLXX. 1, Obj.3).
To what particular authority in the New Law does it belong to determine such things?
It belongs to the Church to determine these things for the right behaviour of the faithful.
Next - The Catechism of the Summa - LIX. OF THE TWO KINDS OF LIFE, VIZ., OF THE ACTIVE AND THE CONTEMPLATIVE; OF THE STATE OF PERFECTION-OF THE RELIGIOUS LIFE; AND OF THE RELIGIOUS COMMUNITIES IN THE CHURCH (A)