If you just have a snapshot state (even with an ideal model of internal interactions from that state) then any thermal contact with the outside will almost instantly raise entropy to near maximum regardless of whether energy is added or removed or on balance unchanged. I don’t think it makes sense to talk about temperature there either, since the entropy is not a function of energy and does not co-vary with it in any smooth way.
If you just have a snapshot state (even with an ideal model of internal interactions from that state) then any thermal contact with the outside will almost instantly raise entropy to near maximum regardless of whether energy is added or removed or on balance unchanged. I don’t think it makes sense to talk about temperature there either, since the entropy is not a function of energy and does not co-vary with it in any smooth way.