Indeed solar panels are colder under load, than they otherwise would be if you turn off the DC disconnect.
In summer conditions, solar panels tend to operate at about 60 Celsius. This is usually considered to be as hot as you expect them to get while operating.
If you throw the disconnect to off, they will heat up to 65 to 75 Celsius. This is due to obvious reasons as you mention. Perhaps 1600 Watts of sunlight are incident on a module that produces 240 Watts. This means that, assuming negligible reflection, during operation, 1360 Watts of power are absorbed as thermal energy. It must be re-radiated or convected away, and the module gets hot to encourage it to do so, as it achieves equilibrium.
A perfect solar module would be completely black. And some of the better modules available on the market today are black-celled. It is usually polycrystalline cells that are blue, and monocrystalline cells that are black. Monocrystalline cells are typically more expensive to manufacture than their poly counterparts, but they have the advantage of efficiency to oppose that. When available space is a large concern, you select a monocrystalline module.
Whatever reflectivity a module may have, which is what causes you to see any non-darkness of them at all, that is what it will have no matter what. It will always reflect this, regardless of the load. The reflections are undesired, but unavoidable in the practical sense.
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The reason why infrared cameras are used in inspecting PV arrays, is that this can tell you a profile of the temperature of the modules. All objects not cold enough to freeze your hand solid, are emitting IR, due to their temperature. More temperature means more re-emission of IR as a means of trying to achieve equilibrium with the background, and at a higher frequency of IR.
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Mike:
the PV module doesn't contain the battery by default. The battery is a load, connected externally.
And batteries can draw a dynamic load too, depending on temperature and state of charge.
PV modules are very dynamic in the power they can produce. It depends on sunlight intensity, cell temperature, and the situation of the load.
Generally, the voltage is a function of the temperature, and the current is a function of the irradiance. When under load, voltage drops slightly from its open circuit value, due to series resistance within the connections and wiring. Current drops slightly from its short circuit value, due to shunt conductances that may be present.
There exists an optimal point on the I-V curve, called the MPP, or maximum-power point, where the product of voltage and current will be a maximum. The inverters and charge controllers are specifically designed to seek this point, as an operating basis, and strategically set the load to match.
Grid-tied inverters let the modules produce whatever they can in full, and then feed it as a supplement AC current to the utility grid. Charge controllers will seek this point, and also work with the battery, so that maximum available power can flow to the battery and DC loads.
Without a charge controller, production is subjected to the dynamics of the PV module and battery, with no optimization technology seeking anything that's best for either.