Commentary for Shabbat 83:4

אבל נותן כו': ת"ר נותן אדם חמין לתוך הצונן ולא הצונן לתוך החמין דברי בית שמאי ובית הלל אומרים בין חמין לתוך הצונן ובין צונן לתוך החמין מותר בד"א בכוס אבל באמבטי חמין לתוך הצונן ולא צונן לתוך החמין ורבי שמעון בן מנסיא אוסר אמר רב נחמן הלכה כר"ש בן מנסיא

even a great distance too [is permitted). BUT ONE MAY POUR, etc. Our Rabbis taught: A man may pour hot water into cold, but not cold water into hot; this is the view of Beth Shammai;<span class="x" onmousemove="('comment',' Rashi: they hold that the lower prevails against the upper. Hence in the former case the hot water is tempered by the cold, which is permitted; but in the latter the cold is heated by the hot, which is forbidden. R. Tam: 'hot water into cold' implies that the cold water exceeds the hot, and therefore cools it, hence it is permitted. 'Cold water into hot' implies that there is more hot water, which heats the cold; consequently, it is forbidden. According to this interpretation this is independent of the question whether the lower prevails against the upper or the reverse, which refers to equal quantities; cf. [H] Yoreh De'ah XCI, 12. ');">¹⁰</span> while Beth Hillel maintain: Both hot into cold and cold into hot are permitted. This applies only to a cup,<span class="x" onmousemove="('comment',' The water being required for drinking, one does not wish it to become very hot. Moreover, a cup is a 'second vessel' (v. supra p. 188, n. 6), I.e., the water is not actually heated therein, and the contents of a second vessel cannot cause anything that comes into contact therewith to boil. ');">¹¹</span>

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