That's a TVS (thermal vacuum switch). It has a sensing bulb that is in contact with the engine coolant.
When the coolant reaches operating temperature the valve opens and applies vacuum to the EGR valve. I think - it might also operate the EFE (early fuel evaporation) valve.
It's hard to tell from the image and without the emissions code (maybe YFC, YFD, YJM) that is shown on a sticker located on the radiator support.
On the falied wire - it looks like the fusible link is still intact. The wire leading into it appears to have been already butt spliced at some point.
Like 89Suburban suggests, butt splicing anything in that circuit is a bad idea.
It looks like there is enough of a stub left to allow you to do a strip, solder and heatshrink repair procedure.
If that lead is the one that goes up to the junction block on the firewall - and it's hard to say from the image - it is a 1mm wire (= 16AWG).