Could Plastic Fumes From Heater Be A Matter Of Concern?

My daughter put plastic markers inside the heater of our apartment. The markers burned in the heater for a while before I noticed the smell. I will try to get the heater cleaned, but I m worried about the health effects on my kids. They are 2 and 5. What should I do? Should I not stay in the apartment until it s cleaned? It s still cold weather so we ll need the heater on.