2003 VW Beetle 2.0 P0118, P0201, P0202, P0203, P0204

I have a 2003 Beetle 2.0 Manual with 53K miles. The check engine light is on and the car has a very hard time starting when the car is warm. After a hard start it will sometimes idle up to 2000 R.P.M., at other times it will fluctuate between 800 and 1500. No problems when starting cold. I have replaced plugs and wires and took it in to Autozone to read the codes. I have the following:

P0118 Engine Coolant Temperature - Circuit High Input
P2181 ...also coolant related
P0201 Injector Circuit Open, Cylinder #1
P0202 Injector Circuit Open, Cylinder #2
P0203 Injector Circuit Open, Cylinder #3
P0204 Injector Circuit Open, Cylinder #4

I did have a frayed wire going to the Coolant Temp. I have also replaced the Fuel Pump Relay more as a gut feel and from discussions from other people with similar symptoms. I am going to replace the Coolant Temperature Sensor tomorrow, but it doesn't seem like that could cause all the problems. Am I off the mark on this? Any suggestions?

I can't imagine a coolant sensor causing the inj. codes. Has any work been done recently where the wiring harness could be damaged? How long ago had the CEL illuminated? Check your wiring harness to and from the injectors first visually, then post back.
Repair coolant sensor harness and replace sensor and post back.

I fixed a wire that was frayed going to the Sensor and then today replaced the Coolant Sensor, it seems to have cleared all the codes. The CEL went off as soon as I started the car after the change. Thanks for the help, I'll update if the light returns.