Hi, Jim. Relays are rated by their contacts (that's the switching part) and coil (that's the part that creates the magnetic force that pulls the switch.
You need a relay whose contacts are rated at least 15 amps at 120VAC resistive.
The coil may be a bit more of a problem. 22.5VDC is an oddball voltage, but it's almost 24VDC. DC relays are usually guaranteed to pull in at 80% or 85% of rated coil voltage. So, nearly all 24VDC relays will actually pull in at 20.4 volts DC and up. I'd be a little concerned, though, about whether your source that will drive the relay would bog down with the load of the relay coil.
Before we do anything else, you should take a look at the docs on your controller, and see what kind of output you have, as well as how it's wired. Many temperature controllers are made to provide a voltage output for a solid state relay (which would be a very good solution for you, except for that "fail-off" business). That may mean it's only capable of pushing 20mA or so into a SSR input. Feel free to contact the manufacturer of the temp controller -- they'll probably be happy to help you find out what you've got from the controller model number.
But assuming you really do need a 24VDC coil relay, let's see if we can give you a hand with your immediate problem here. The Tyco/Potter&Brumfield T92S11D22-24 is a great relay for industrial control applications. It's DPDT (double pole, double throw) contacts are rated for 30 amps at 120VAC resistive, and has a 24VDC coil that's
350 ohms. It's also available at Allied as Stk.# 886-0149. I like it because the contacts aren't open to the air (nothing messes up relay contacts faster than ceramics dust -- it prevents them from closing fully and leads to a miserably short life), and it has faston connectors. Bolt it down with two screws, plug in the faston connectors, and you're done. I like that kind of solution.You can download the P&B data sheet from the website. This will help you wire it up, as well as giving you a bit of an intro to how relays are spec'd.
By the way, see if you can get a 330 ohm, 3 watt or more resistor before you order your relay. Put it across your 22.5VDC source and see if it bogs down below 21VDC. If the voltage holds up there, you're good to go. If it does bog down, it's probably a SSR driving output. In that case, you might want to consider a smaller relay with a higher ohm coil or look to some other means of driving the relay coil (possibly a transistor).
Also, you should put a 1N4002 diode across the relay coil to absorb the inductive kick of the relay coil when it turns off, so whatever's doing the controlling won't have to.
Feel free to post again with any additional questions, especially if you have a SSR output on your controller. There are ways to get around that so you can use a relay instead.
Good luck Chris