Is there a specific thermometer to check soup temperature?
This is fine, albeit inconvenient
Don't make contact with the bottom of the pot, for the reasons described. Stirring can help make the temperature more uniform. 
You could try a candy thermometer. But most soups aren't sensitive enough that you need to be super careful -- just poking it with a Thermapen or something similar every few minutes is probably more than enough. You can also get an oven-safe dial type thermometer and thread it through a binder clip or similar clamped to the pot, or an oven probe type thermometer (the kind with the probe on a cord). 


For an overview of different thermometer types, see this USDA link.