I have a CB. ,Solenoid on it is a Dormeyor, P. no. 2005-m-1, 120 v,60HZ Duty Cont.
I've worked with this type of solenoid for many years on my job. I looked up the specs on the model I have and found nothing for temperature rating. So I figure you have another brand or type. Out of all I've worked with I've never seen one that I would install in 400 f and expect it to operate very long. My CB has an insulated door ans so far I've never had an issue with heat in that area. If you will post the name and part number on the type you use. I may need one for a hot area some time and then know what to buy.