Quoteyou could use the ARef input and analogReference() function to scale the Arduino input to 25 or 30 millivolts full scaleThe minimum recommended reference is around 1 volt. Below that Arduino is too noisy to produce reliable results. Note also that any attachment to a real thermocouple must use an "ice-point" reference compensation or else you will never know whether you are measuring the temperature at the thermocouple, or the temperature at the junction point. That is one of the downsides of using real thermocouples.
you could use the ARef input and analogReference() function to scale the Arduino input to 25 or 30 millivolts full scale
Honestly, if you *really* need 1000 samples per second, the only tool that would do readily do that is an oscilloscope or a dedicated data acquisition system. Nothing really converts and sample that fast, nor does it make sense to in an industrial control setting, which is what most of these tools are.