Heat is transferred from one object to another by conduction, convection, evaporation, and radiation. #3 is the only one to mention radiation, which is key to the old thermoses I brought to school that have mirrored/silvered glass on the inside. They also shattered if you dropped them, which dramatically reduced their popularity since no one wants to drink crushed glass! The mirrored/silvered surface works by reflecting the radiant heat, which consists of light in the infrared spectrum, back towards the liquid. Think of the night vision goggles used in movies and the military that "see" the infrared heat coming off of your body. The thin, silver, emergency "blankets" sold now work the same way, reflecting your body heat back to you. To keep your coffee warm the longest time, you want to block all 3 pathways. The double wall reduces heat transfer by conduction and convection. A vacuum middle layer would ideally block both these processes much longer, since there are no molecules in a vacuum to transfer the heat. Interesting comments that the double steel wall mugs work better. I think steel is a better conductor of heat than glass or ceramic (which can have tiny "microbubble" air pockets in its makeup). Think of the steel fins in car radiators, air conditioners, as well as laptops and computers, used SPECIFICALLY for their rapid transfer of heat!
Lastly, the steam coming off of your fresh mug of hot coffee (that makes it look so good!), is evaporation taking place at the coffee and air interface, as energetic water molecules break loose and launch into the air. Evaporation sucks a whopping 540 cal of heat from your coffee per gram of water evaporated. Much faster than when the coffee looses heat by direct contact with a cooler surface (conduction), which is only 80 cal per gram of water. A simple lid cuts the evaporation way down here. But then it still condenses on the underside of the cooler lid surface, giving its 540 cal to the lid. But, this is still better than losing it all to the air in the room. SO, the best coffee mug would be a double wall of material with the lowest heat transfer rate, WITH a vacuum between layers, AND with a lid. Actually, I failed to mention one other factor. The heat conducted from the coffee, to the bottom of the mug, to the table surface, which is the only place the mug physically contacts another solid material. This is why all coffee cups have a raised lip around the bottom, since this reduces the amount of coffee mug touching the table. To be extreme, you could make your cup with little spiked legs that would reduce the surface contact by 90% or more! To go even further, two inventors shown on the Sharks TV program, designed small cubes of a material that initially absorbs heat from the coffee, and then slowly releases it back to the coffee as the temperature of the coffee goes down. yes, my BS was in Biomedical Engineering. And as a doctor now, heat transfer is key to treating hyperthermia and hypothermia.