I think glancing at it just before you start the takeoff roll, then again after
you reach a safe height (300 feet, say) and every 20-30 seconds after that would
be adequate. But - I think you are right that detecting the smoke or flame might
be very difficult in the engine bay, which is my problem (The FES pilots might
have success in the battery compartment, though). Probably need to do some smoke
tests on the ground and inflight with the engine running.

I have a FLIR ONE for my iPhone, but mounting it in the engine bay with a
Lightning cable to the front isn't practical, since it can't be turned on remotely.

I couldn't find a cheap camera ($200) online that could be used the way I'd like
to, either.

Depending on how many resources you want to throw at this, the MLX90640 is reportedly a decent 24x32 FIR camera which interfaces over I2C. So you could stream data to a microcontroller, or even an embedded computer such as a Raspberry Pi (although please use an industrial spec variant) and then forward that data to the cockpit. I'd do a static background subtraction so that you're only looking at heat blooms. One of the nice things about this approach is you can have the screen be completely dark except for anomalies. Much easier to set up automated warnings in this case.

A camera can only see what it's pointed at, so if the ignition risk is hidden from view a single camera might not be useful. How that affects things I can't say. However, you might be able to set up strategically positioned mirrors so as to see many sides of the engine bay. Since you don't really care if the image is distorted, it won't bother you.

Testing is probably straightforward, since you could rig up a power resistor glow red-hot while in the air, so you could see what kind of response you actually get when everything is shaking and heating up.

In terms of hardware, this R&D effort will likely cost $200, including the screen. In terms of time, it's probably pretty straightforward as well, especially if you're comfortable with hacking together various scripts from blogs and stackoverflow.

Before I jumped on the camera train, though, I'd give careful consideration to what it means to detect a fire. You might find that the kind of fires you want to detect are far earlier than would be seen by a camera. I don't have a firm concept of fire detection (What does it mean to detect a fire? How do we even define "fire" in this context?) so I'm at a loss for what are the precursors to a fire.Â*