Yes, wires to the amplifier directly. It seems like a MAX31855 should work right, based on what little documentation Campbell Scientific provides. It's a bit of an odd way to do it but not unreasonable.
The MAX31855 is going to give you back values in "temperature readings" which you'll then need to convert back to millivolt values. NIST provides charts
for that. FYI I'm linking the Type K thermocouple chart here because that is the type of MAX31855 amplifier that Adafruit sells. You'll then need to convert those millivolt values to solar radiance, but I don't immediately see where Campbell Scientific provides that information.
Mathematically converting temperature to millivolts is a really ugly formula -- you can search "thermocouple coefficients" to get a feel for that. If you're as mathematically inept as I am you might want to try MultiMap()