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Is it permissible to heat non-food items on Shabbath? Assume the method of heating is to use an existing heat source (a blech, or the top of a crockpot or hot water urn).

Would it matter if it is for heat therapy or for general warmth?

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Cooking is forbidden for non-food items as well. See Mishna Berura 318:1.

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    +1, correct; whether one can heat it, then, as asked in the question, would depend on the same rules as whether one can heat food.
    – msh210 ♦
    Commented Jun 29, 2012 at 19:42
  • Does it matter that in all of those cases (IINM), the Mishnah Berurah is talking about processing the thing somehow through extreme heat? In this case it's just heating the thing to have it hot in its current state. Let's say it was a perfectly clean and dry rock used to warm your feet in bed in the winter. Not smelting metal or drying out wood or making anything glowing hot like an ember. If my blech is Yad Soledeth Bo, you are saying that if I poured water from my urn and intended to heat the rock in the cup of water, I'd have to use another Keli?
    – Seth J
    Commented Jun 29, 2012 at 20:17
  • @SethJ I don't really see why not, although your application is not exact. Once [yad soledes bo] water is poured from the urn into a cup, the cup of water is a kli sheini, so you could simply put the stone in that. You just couldn't pour directly from the urn onto the stone, because that would be iruy kli rishon.
    – Dov F
    Commented Jun 29, 2012 at 20:31
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    @DovF All of those cases are Toldot Mevashel because they use heat to improve the item ("creative labor"). I don't know that stam heating a rock is in that category, nor do I think that Yad Soledet Bo is necessarily the shiur for this purpose, ie drying out wood might be chayav at a lower temperature (if the metziut is such that the wood would dry; I have no idea what that is). (All complete speculation.)
    – Double AA ♦
    Commented Jun 29, 2012 at 21:55
  • @DoubleAA Seth's case isn't heating to improve the item? With regards to your second point, I don't believe we ever say something is bishul by less than yad soledes (even if there's a tzad to say it by things that aren't kli rishon, they're still yad soledes). One proof is the case with the herring in cold water. I'll try to cite sources later - I have to run now.
    – Dov F
    Commented Jul 1, 2012 at 3:07

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