Thermoset plastics will not melt and will release all sorts of magnificent things when heated.
they have a section discussing different kinds of plastics, and simplifies the information to the notion that if the plastic lacks a recycling symbol then it is in the category of 'unrecyclable'
unless you're worried about getting it out in the air at all, also outside. in which case I'd start with avoiding campfires, (certain types of) barbecues and petitioning your neighbours to stop using their fireplaces, good luck :p
and like others said, it's not a very high temperature.
about that "thing that mgiht be carcinogenic or such", do you mean phtalates? i might have spelled that wrong, the plastic-softener compound. it's not present in equal amounts in all types of plastic, definitely not those intended for food-containers. if it's present in higher amounts you can easily smell it, it's that particular smell that is on that soft, rubbery, "soft-grip" plastic, especially when it's new.
btw not even living itself is ever "100% healthy" :) it's always a trade-off, and in this case, it seems pretty good, trade-off is for the planet and the children :-)