Corten is in essence a variation of high strength-low alloy construction grade steels with additional Cu to enhance corrosion resistance and would not normally be considered for elevated temperature applications for the following reason:
The mechanical properties of the high-strength low-alloy steels depend on their hot rolled condition. These steels are not further heat treated except for annealing, normalizing or stress relieving, applied as required to facilitate cold forming. The heat treated grades depend on either precipitation hardening or quenching and tempering for development of mechanical properties. Ref: 8th Ed Metals Handbook Vol. 1 p87.
In other words, if you heat these steels the properties are going to change. However, there could be data on what these properties are at elevated temperatures but it does not seem likely given the above excerpt and having seen how these alloys are typically applied where min yield of about 50,000 psi is required.
If you are only looking at a few hundred degrees F, probably no problem. Otherwise you should probably be looking for a heat resisting alloy.
hope this helps,
Leonard Jesus is the WAY