Normally, I'd say these two codes wouldn't be related, but googling the combo seems to indicate you're not the only one seeing these two codes in conjunction (not so much on a Vette, but OBDII code designations are mostly universal). So maybe there is a connection...
The P0128 is what you should attack first. It sets when the coolant temp doesn't get warm enough, or remains warm enough. It's there to indicate a faulty thermostat, but a bad temp sensor could also be the culprit. You can probably determine which by simply watching the coolant temp as the car warms up. The coolant temp should reach 167° within about 15 minutes of driving, and not fall below that point as long as it's running. If it's below that temp, this code will set. If the gauge/DIC seems to be giving a valid temp indication (meaning not dead or pegged), and it is just slow to warm up, then it's possible your thermostat is stuck open.
The P0410 is an AIR system code that affects both banks of the engine. It usually points to a problem with the air pump, or with the vacuum-actuated shutoff valve between the pump and check valves on the engine. How this code is thrown is by the PCM monitoring 02 sensor data. When the AIR pump is commanded on, there should be air pumped into the exhaust manifolds, and the PCM expects to see the 02 sensors reporting this leaner condition. When the 02 sensors (both sides) don't detect that additional air in the exhaust, this code is thrown.
The reason I suggest chasing the P0128 first, is because the PCM injects more fuel when the engine is cold, it runs richer, which could mask the (expected) lean condition provided by the air injection. If so, it seems possible the P0410 could be a result of that abnormal temperature, not it's own separate problem.
That's just my theory, and it could be "technically not possible", but I can't think of any other reason why these two codes might be related or set simultaneously.
