Why does the Atzel bury his hand in the plate?
Rashi #1: When they remove a hot pot from the fire and emptied it, he warms his hand in it, and it seems to him "Bishelu ba'Siros uva'Devadim uva'Tzelachos 1 " (Divrei ha'Yamim II, 35:13).
Rashi citing R. Yitzchak ha'Levi: Tzalachas is Arame'ic. The Targum of "va'Yvaka" (Bereishis 22:3) is v'Tzalach. At a time of cold, hands are 'cleaved' (chapped).
Rashi #2: Tzalachas is the opening of a cloak. He buries his hand in his garment.
R. Yonah: This Sefer often discusses laziness next to fear and Chachmah, for they need Zerizus and Gevurah. Zerizus leads to Nekiyus (Avodah Zarah 20b). The verse depicts that an Atzel does an act, and does not finish it. From here you understand regarding fear - one who does a Mitzvah and does not finish it, he is called lazy in Shamayim's work. If one began a Mitzvah, we tell him to finish it (Yerushalmi Pesachim 10:5).
Malbim: This illustrates "Ta'avas Atzel Temisenu Ki Me'anu Yadav La'asos" (21:25). His hand refuses to move. If hunger forced him to send his hand to the plate to take food, he buries his hands there for security against what forced him to move it. He fears to move it from there. He leaves it there and does not return it to his mouth. He will be hungry, and not move his hand.
I.e. as if he has hot food. (PF)
