Can I look inside an oven and measure the target temperature with an infrared thermometer?

Yes, but you have to consider the problem of reflections. Usually the oven is hotter than the target. The target has some reflectivity so the thermometer measures the emitted energy as well as the reflected energy and indicates too high. This can be eliminated by using a sight tube, or possibly measuring the target at the exit of the oven. For glass, plastic films, and paper applications selection of the right thermometer can eliminate the reflection problem without a sight tube or looking at the exit of the oven.