Cookies are soft in the middle, even though the edges are browned
If the edges burn and the center is undone, it means the heat didn't have enough time to reach the relatively cool center before the edge was too hot. The temperature gradient depends on the amount of heat from your oven and the size of your cookie - and to some degree on the thermal properties of your cookie sheet. 

You have mentioned the two "usual suspects" in your question:

Oven temperature and convection.


Ovens thermostats are notorious for being quite a bit "off". A good oven thermometer placed on the middle rack can give you a precise measurement and even helps you to recognize whether it's a "fluctuating" issue or whether your oven is generally running high or low.
Convection can change the way the oven heat is distributed to your cookies. Most recipes I'm familiar with suggest lowering the temperature by 25C / 50F if using the convection feature. This is not necessarily always the ideal solution, some types of cakes simply turn out better without the convection feature. (But that's a gigantic can of worms that I won't be opening here: Many bakers have their own view on this.)


If those two don't help, look into the type of cookie sheet and the temperature of your dough when it's put in the oven - chilled dough will behave differently from room temperature dough, for example.