Does color have an effect on thermal conductivity?

If you are talking about heat transfer through the bowl by conduction from the stove, adding a layer of paint, regardless of its color, will reduce the steady state rate of heat transfer through the bowl not increase it. But the effect will be very little because the paint layer is so thin.

A cross section of wall of the bowl consists of the thickness of the layer of paint plus the thickness of the bowl material itself. Then the total thermal resistance of the cross section will be sum of the thermal resistance of the paint plus the thermal resistance of the bowl. The addition of paint increases the total thermal resistance so it reduces the heat transfer rate.

The electrical analogy where current is analogous rate of heat transfer, voltage is analogous to temperature difference and electrical resistance is analogous to thermal resistance, adding electrical resistance to a given series resistance circuit with a fixed voltage source reduces the current.

Hope this helps.

The effect of external surface colour on the thermal behaviour of a building has been studied experimentally as well as theoretically. Experiments were performed on scaled down units of 1 m3 volume, under different conditions; namely (i) completely tight building, (ii) effect of opening the door and (iii) of an overhang on the window for complete shading throughout the day. A computer simulation programme, based on periodic solution of the heat conduction equation, was developed to yield the time variation of the room temperature corresponding to the given meteorological parameters. As expected, the black painted enclosure recorded a maximum of 7°C higher temperature than the corresponding white painted enclosure during hours of maximum solar radiation, while during the night the two enclosures showed nearly the same temperatures (being the light weight constructions). The experimentally observed temperature meaasurements were quite consistent with the theoretical calculations within experimental accuracies (±2°C). The same software when used to simulate the behaviour of a normal sized heavy structure, predicted 4°C to 8°C higher temperature throughout a period of 24 hours for a black coloured surface than the corresponding white one.