Is it possible to use planar binding like this?

[Braininthejar2]

The spell planar binding is usually used to negotiate a single task, after which the creature receives payment and comes back home.

Is it possible to have it work as an extended contract, with continuous exchange of services?

Basically, my wizard got roped into maintaining a large hospital in the capital, and I wanted to summon a fire elemental and convince it to live in our basement.

Since it has INT of 5, not very good at negotiating, and hasn't got much motivation beyond burning things (difficult on a plane made of fire) I wanted to offer it a deal: It stays with us and provides the heat for our boiler, and in return it gets to incinerate our trash (which we might not want to just dump away, due to biohazard issues)

So, is it legal, and if not, what is the lowest level spell that could do it?

[Psyren]

"Heat a hospital" would count as an "open-ended task" and thus last 1 day/caster level. At the end of that time, you could bind the same or a different elemental, renegotiate price, and repeat.

You can theoretically do this as long as you have rewards a fire elemental would care about. A fire elemental "takes joy in burning the creatures and objects of the Material Plane to ashes", so I would suggest allowing it free reign of the basement/cellar for the duration of its stay, allowing it to roast any vermin or pests it comes across. Not only would it enjoy incinerating all the rats and flies, this doubles as pest/disease control for your hospital. In addition, have it run the incinerator to dispose of any cadavers, disposable equipment, hazardous waste, spoiled food, leftover organs or any other hospital byproducts.

Your biggest problem would be keeping it properly contained so that it can't rampage and burn down the building, so take precautions there and be sure to stipulate such prohibitions in the binding.

[ExLibrisMortis]

If you want to make the binding permanent, you can try crafting a permanent magic basement of planar binding (2000 * 4 * 7 * 0,5 = 28.000 gp), and convince your DM that the immovability of the item warrants a 50% cost reduction (7000 gp in materials and 560 xp, just pretend that 7000 gp is payment for the elemental). This is more of an artificer thing, but it can work quite well, if you're set up for crafting already. Note that this is not strict RAW: it is a reasonable way to implement a permanent binding using existing mechanics, but your DM may not like it.

Alternatively, you can use plane shift to actually go get an elemental from the Plane of Fire, and pay/employ it without using the whole binding process. You can use hallow (duration: one year and a day) to apply some permanent spell to the dungeon that makes the elemental unable to leave.

[daremetoidareyo]

"Heat a hospital" would count as an "open-ended task" and thus last 1 day/caster level. At the end of that time, you could bind the same or a different elemental, renegotiate price, and repeat.

You can theoretically do this as long as you have rewards a fire elemental would care about. A fire elemental "takes joy in burning the creatures and objects of the Material Plane to ashes", so I would suggest allowing it free reign of the basement/cellar for the duration of its stay, allowing it to roast any vermin or pests it comes across. Not only would it enjoy incinerating all the rats and flies, this doubles as pest/disease control for your hospital. In addition, have it run the incinerator to dispose of any cadavers, disposable equipment, hazardous waste, spoiled food, leftover organs or any other hospital byproducts.

Your biggest problem would be keeping it properly contained so that it can't rampage and burn down the building, so take precautions there and be sure to stipulate such prohibitions in the binding.

maybe a self resetting trap of halaster's fetch?

[Beheld]

You can't actually make a Planar Binding permanent, but you can do a lot of things.

1) Planar Bind a Fire elemental, don't actually make any deal, let him sit there for one day per CL, and then find a way to funnel trash on him so he burns it.
2) Planar Bind him and have the service be burning things to trash, you don't actually have to pay him anything, so don't. At the end of one day per CL, Planar Bind another one the same way.
3) Go to the plane of fire, beat him up and put him in a portable hole, plane shift and TP back. Use the spell Binding to make a Hedged Prison, Continue as per 1.

[Emperor Tippy]

"Heat a hospital" would count as an "open-ended task" and thus last 1 day/caster level. At the end of that time, you could bind the same or a different elemental, renegotiate price, and repeat.
Yes, but "heat this hospital until ten billion days have passed or I release you from this task" is not an open ended task and thus works just fine.

There is no RAW requirement that the task a creature is bound to complete need to be feasible to complete in a short amount of time, just that it must actually be finite.

[atemu1234]

Get a necromental to kill a fire elemental, then command or find another means of controlling the resultant undead?

[Psyren]

Yes, but "heat this hospital until ten billion days have passed or I release you from this task" is not an open ended task and thus works just fine.

There is no RAW requirement that the task a creature is bound to complete need to be feasible to complete in a short amount of time, just that it must actually be finite.

While you're correct that an interminable yet technically finite command isn't "open-ended," it could just as easily be "unreasonable" and get rejected entirely. Certainly if I were the GM I would seize upon the latter. It's a pretty poor deal for the creature to accept anything that would keep them in thrall longer than you could hold them with no limit at all; at the very least, you'd be forced to pay them twice if not more often.

[Ahus]

If you're "maintaining" the hospital I would just suck it up and cast the spell every few weeks as part of your maintenance...

That said this sort of thing is precisely what the Bind Elemental Feat from Eberron is designed for.

[Florian]

I´m with Psyren on this one. "Open Ended" mostly means a specific task that will happen in the future and is not strictly specified. (aka "When we meet the Dragon, then...")

The case we talk about here is either crafting a custom wondrous item or creating something like a "furnace golem".