I am fairly new to deep learning in general and I am currently facing a problem I want to solve using neural networks and I am unsure if it is a classification or regression problem. I am aware that classification problems are about classifying whether an input belongs to class A or class B (or class C ...) and regression problems are about mapping the input to some sort of continuous output (just like the house pricing problem).
I basically want to measure the body temperature of a person using a simple video camera. To me, this seems like more of a regression type of issue rather than classification, because of the actual continuous result values I want the neural network to produce from the input video frames, e.g. 39°Celsius. But a question that came to my mind was: What if I use every integer value in the range from 35°C to 42°C as a possible output class? This would make it a classification problem, am I right? What would be the correct approach here and why? Classification or regression?