I'm unsure as to how to set the input up to the LTC2983 using an AD590 powered by 5V?
My plan is to apply 5V to the + terminal of the AD590 and attach the - terminal to a 1k Ohm to GND. I then plan to connect the - terminal to a channel input of the LTC2983 set up as a direct ADC measurement set up as a single ended input. Is there a better approach than this?
That sounds like a good plan to me. The single ended input range is 0-1.25V (VREF/2) so you're good to go there and the input buffers are very high impedance so there shouldn't be any loading of the 1k resistance.
I'm assuming you need all 20 inputs of the LTC2983/2984 - if not, you could use the LTC2986 which can use the AD590 as an active analog temp sensor, doing the (admittedly simple in this case) 1mV = 1 K translation into degrees C for you direclty, as well as use the AD590 as the cold junction compensation sensor if you are also using thermocouples.
In this case I only need one of the channels. I'm using a routed board in a system that has the LTC2983 on it. But in a multi-channel use case I can see doing this for up to 4 of these sensor types.