How does my spinal cord know to take reflexive action? As in, how does my body know that a stove is not hot enough to warrant a reflex? Is it because there isn't a sudden electrical surge going through the nervous system?
It's not that your body knows, exactly, but that one's body is wired in such a way to support reflexes. There is a sudden electrical surge (electrochemical, actually) but it's more compartmentalized than "the nervous system."

Divide the nervous system in two: we've got one section containing our brain and spinal cord. That's called the central nervous system, or CNS. Everything else is our peripheral nervous system, called the PNS. 

I'll use the stretch reflex because it's the one I'm more familiar with, but the same goes for all spinal reflexes. Our muscles actively contract, and we need a mechanism to make sure they don't extend past a certain point. The stretch reflex is such a mechanism: when that rubber hammer hits the tendon below the kneecap, the thigh muscle gets stretched. In turn, this causes the knee-jerk reflex as that muscle gets a sudden jolt of "oh my god we don't want that to stretch or else we might not be able to run if we need to or it might damage the muscle or..." (you get the idea, surely).

The reflex takes precedence above conscious thought. Usually. How it does this is through bypassing the brain. Think of how it might work otherwise: hm that stove is hot, I need to get away from it? There'd likely be far fewer humans in the world if that were the case. Instead, the surge (called an action potential) travels straight from sensing to action--preserve the organism, then it can think about whatever just happened.

As far as when to jump or not to jump, neurons either fire or they do not, as per the all-or-nothing principle. If there's enough stimulus (if it's hot enough), then that'll happen.