The amount of power going into a device such as an LED or a diode is the voltage times the current.

LEDs tend to have higher voltage drop than rectifier diodes. For example, a 1N4004 might drop 0.7V at 0.35A (245mW) but a blue LED would drop more like 3V, so it would be consuming more than 1W at the same current, and if the packages were identical it would get much hotter.

The LED will actually run somewhat cooler than you might expect because some of the heat is carried off as light rather than as heat.

The amount of power going into a device such as an LED or a diode is the voltage times the current.

LEDs tend to have higher voltage drop than rectifier diodes. For example, a 1N4004 might drop 0.7V at 0.35A (245mW) but a blue LED would drop more like 3V, so it would be consuming more than 1W at the same current, and if the packages were identical it would get much hotter.

The LED will actually run somewhat cooler than you might expect because some of the power is carried off as light rather than as heat.

If the LED was 100% efficient, then it would not heat up at all- all the incoming power would be converted to light. Most LEDs are probably in the 5%-20% range, so most of the incoming power still leaves as heat.