Tank, without knowing more about your setup, I'm just speculating here. In my CG, the grate temperature is usually higher than the temp indicated by the thermometer in the lid. The difference, though, can vary depending on the circumstances. For example, if it's windy, if the pit is in the direct sun, etc.
As to smoke, smoke in itself isn't an indicator of the temperature at the grate. I've had smoke pour from mine, shortly after reloading charcoal and chunk. In one case, I waited too long and the grate temp really dropped low. As the grate temp rose, the smoke dispersed. By the time the grate temp got back to where I wanted it, most of the highly visible smoke had disappeared.
Think of the smoke from a campfire, as a way of explaining. When a campfire is buring well, there isn't a lot of smoke. Yet, there's a high output of heat. Let the fire burn down too much. Then, add some damp wood. For a while a tremendous amount of smoke is produced, yet there's very little heat. The heat will increase once that damp wood begins to actively burn. The hotter the fire gets, the less visible smoke is produced.
Hope that makes sense.
To know for sure what's going on with the temperatures, get a thermometer that will measure grate temperature. It can be an oven therm that sits on the grate. It can be a candy therm or a turkey fryer therm inserted through a hole or vent. (Use a cork to keep the stem from touching the grate). Or it can be a probe inserted through a potato and placed on the grate.
And, in closing, check the calibration of thermometers. Insert the stem in boiling water. It should read 212*F (adjusted for altitude, if applicable.) If the therm is off and can't be recalibrated, just take the difference into consideration when reading the dial.
Hope this helps a bit. Hope your chicken turned out OK.
CharGriller Super Pro SFB
Sunbeam gas grill