Yes , and they have plenty of strategies to cool off, as in the Antarctic summer sun, penguins are roasting. They then bristle their feathers to increase airflow, and spread their fins to the sides. Sometimes they are so hot that their fins turn pink, and they stretch out on their bellies against the ice , like dogs. Babies lie on their backs. Jumping into the water is another solution.
The only "ice penguins" are the Emperors and Adelie. If they are hot, imagine those on the South African and Argentine beaches. They dig nests under the sand to get rid of the sun, and their feathers, arranged like tiles, are short and dense to make them waterproof. Underneath they have a layer of fat several centimeters long. That is why it is difficult to see a penguin shiver from the cold.
