I haven't looked at a Dometic in years. Not sure what you mean by thermal limit switch. My Norcolds don't have one that I know of. I've heard other talk about an aftermarket limit device, not sure how it works.
You didn't put your model number in the post. These guys need that to give you more specific info.
The 5 amp is probably for the AC electric heating element. 3 amp for the controller board. Both fuses being blown is a bit confusing.
If your controller board isn't getting power you can't run on gas either.
When you replaced the fuses, did they blow again?
You need to measure the resistance of the heating element. They vary depending on the model. All of mine were around 300 watts. Which would be about 50 ohms.
That would make normal operation around 2.5A. If your blowing the 5A fuse yours would be around 25 ohms or less.
