Why is the Sun so bright, but you can feel it far away?
The answer to your first question has to do with luminosity. It's a measure of power, the energy given off by an object in a certain amount of time, which you can think of as brightness. The more luminous the object, the brighter it appears.

We can treat the Sun as an idealized object called a black body, which emits thermal radiation according to something called the Stefan-Boltzmann law. Assuming the Sun is spherical, with a radius $R$ and temperature $T$, then its luminosity $L$ is
$$L=4\pi\sigma R^2T^4$$
where $\sigma$ is the Stefan-Boltzmann constant. The important thing here is that $L\propto R^2$. If the Sun was the size of one of your furnaces, it would not be very bright; if the furnace was spherical and could be treated as a black body, the two would have the same luminosity.

The Sun, however, has a radius on the order of about $7\times10^8$ meters. I don't know how big the furnace is, but I'm assuming it can't be larger than ten meters, to an order of magnitude. First, that's a size difference of about $10^7$. Second, we square the radius when determining luminosity, meaning that there's a difference of a factor of $10^{14}$. To make this a bit more meaningful, the Sun is then essentially one hundred million million times more luminous than the furnace, even though the temperatures are the same.

I feel like your second question may be a duplicate of What is the temperature of outerspace? (see also the questions linked therein), and Run like hell has already tried to address it. barrycarter's comment, though, is spot-on. The flux from the source, $F$, drops off via the inverse-square law - that is, at a distance $r$ from the source,
$$F\propto\frac{1}{r^2}$$
Remember how we just established the power (pun intended) of squaring a large quantity? Interstellar distances are enormous; the nearest star system, Alpha Centauri, is roughly $10^{16}$ meters away, or ten thousand million million meters. Now square that distance. That's a tiny factor - even when multiplied by the luminosity of all three stars, which combined is still on the same order of magnitude as the Sun.