Spanish hot chocolate and Italian cioccolata fiorentina both use cornstarch as a thickening agent. Both are used more for dipping or sipping (churros in the former case), however you could easily just use less cornstarch to make it more 'drinkable'.
Try a teaspoon of cornstarch, mixed with a little cold water, added to the milk when you boil it.
As Kate Gregory suggests, you could also use full-fat milk, or loads of shaved chocolate.
Very simple: don't store your chocolate in the fridge. The ideal temperature for setting chocolate is 20°C. You can store it at less or more than that, but not too much. Setting in the fridge results in bad chocolate. Remember, when you work with chocolate, exact temperatures are extremely important.
Here a loose translation from a good article on chocolate/couverture coating:
This is the usual case. You only want a temperature difference of 12° to 13° between the chocolate and its environment as well as between the chocolate and the confect interior.
If the interior is colder than the room, the setting will happen "inside out". The cocoa butter film which gives a confect its shine will build on the inside, leaving the outside looking dull.
This is a really good case for some types of confect, but you can't do it with most types of filling (definitely not with strawberries). Cooling from the outside gives you a beautiful shine.
If you want to achieve a good shine, it is possible to put the confects in the fridge for a short time, but only after they have cooled to 20°C at room temperature. Don't let them fall to fridge temperature, take them out at 15°C. The continued cooling from the outside is beneficial.
This shouldn't happen. The temperature difference is too small, and the confect doesn't set quick enough. In this case, cocoa butter pools on the surface and creates a yellowish layer after it hardens.
When you make your confect, you should time the first piece. The setting should need 10 minutes. If it is less, you don't get all the possible shine. If it needs more, it will get grey or whitish yellow.
Best Answer
You can either maintain the heat level through a heat source served with the food at the table or you can add a neutral-tasting oil to the chocolate mixture such as canola(rape seed) or vegetable oil. Adding another fat will also help in preventing scorching of the chocolate.
Also the addition of some dairy to create a chocolate "sauce" can be a solution as well, but remember that fondue is about heating(and even cooking) food. A cold bowl of chocolate, even if it is liquid at room temperature, probably isn't going to be as enjoyable for your guests.