1st even though they are shiny they still absorb some light (both visible and infrared).
2nd they have small heat capacity so they warm up fast even if the amount of heat they capture is not very large.
3rd (and most important) Your skin does not feel the temperature of the objects you touch (you have no nerve endings in the objects). Your skin feels its own temperature. When you touch a hot object heat moves into your skin warming it up giving you the sensation of warmth. Metals are good heat conductors so they allow heat to flow fast into your skin increasing the sensation of warmth. By the way, that's also the reason why metal will feel colder than wood in cold weather.