Mug cozies do work to keep your coffee or drink hot in your mug a bit longer.
The mug Cozy also helps to keep your hands cool from touching the hot mug.
Although a mug cozy won't keep the drinks in the mug hot for too long they do work for a short while and although you to keep your drink hot until you finish it.
Another way to keep your mug warm and your drink warm in your mug is to use one of those tabletop electric candle warmer things.
They are the right and perfect size to sit a coffee mug on and they keep the mug and drink warm.
I use one on my desk to keep my coffee warm in my ceramic mug and they do work great.
The candle warmer plate is basically a small hot plate that is used to warm candles but they can also be used to keep your coffee warm and they don't use that much electricity and are cheap to operate.
They also make coffee mug warmer plates as well but the candle warmer if you have one also works.
Another option which I also use is my electric filled radiator heater I have in my living room near my recliner.
I sit my ceramic coffee mug on the electric filled radiator heater and the heat given off by the heater keeps the coffee hot.