As it depends on a number of factors, including where you are in the world, you should check in with the fire department to see when they think it will thaw. At least, when I lived in Minnesota, it was the fire department you called... there must be a local government agency that could let you know the dangers. I moved down to SoCal, so I never have to worry about ice!
If you even *think* that there's thin ice, don't go on it, particularly on a river. If you break through ice on a lake, you can pull yourself out. If you fall through on a river, the current pulls you under the ice, and you drown. Which would suck.
The most important factors in how long it will take to unfreeze is the thickness of the ice, the temperature of the warm spell, and how long the warm spell lasts.
Have fun, stay warm, and stay safe!