Anti icing systems that use bleed are either "run-wet" or "evaporative".
Run-wet systems heat the surfaces to below the water boiling point, say 140-160F. Supercooled drops hitting the surface are kept from freezing on the leading edge, but can run back and refreeze on the unprotected areas. In that case the "lowest" temperature is whatever keeps the water liquid until it's off the protected surface.
Evaporative systems heat the surfaces to above the boiling point of water, say 220-230F, so the supercooled drops that strike immediately turn to vapour, like spitting on a steam iron, and no ice can form farther back. In that case the lowest temperature is the boiling point plus a margin.
You use an evaporative system if you can't tolerate runback ice (otherwise you'll use a cheaper and less demanding run-wet system). On a wing, this will be related to the airfoil's stall behaviour with runback ice, and a non-slatted wing with a supercritical airfoil (which tends to have poor stall behaviour) will typically have an evaporative system. If you can live with run-back ice because the wing is tolerant ice forming aft, or if the wing has a slat system that makes it tolerant of ice forming aft with slats out, you may use a run-wet system because of the lower heat demands and costs.
On cowls, same sort of thing; you'll use a run-wet system if the engine is not too sensitive to runback ice forming and distorting the flow on the inside surfaces of the cowl or breaking off and hitting the fan blades, or if it is, an evaporative system, that will keep the cowl leading edges in the mid 200sF.
On the General Electric CF-34, the bleed that supplies the cowl is blended with ambient air to cool it down using an air ejector at the entrance to the cowl piccolo system, where the hot air is dumped into a larger duct from an ejector nozzle, which pulls ambient air in with it and mixes them together. By the time the air is entering the piccolo duct, it exits from little holes cooled off quite a lot, and then it has to fill a space and transfer heat through the skin to the leading edge outer surface, so the it might still be 300-400F (after leaving the bleed port at 500F) or more even when being dumped into the leading edge of the cowl, in order to keep the leading edge skins heated to more than 220F.
If a cowl has a run-wet system, these temps will be much lower obviously.
The upper temperature limit is mostly related to the temperature tolerance of the leading edge and adjacent structure (such as heat treat state and the effects of heating/cooling cycles on the structure etc).