Fire will burn different colors depending on the chemical reaction of the material burning. If you are just burning wood, the color is probably due to the heat of the fire. Relatively cool fires burn red, then orange, yellow, green, blue, indigo, and violet as the fire gets hotter. The reason we usually don't see the last three hottest colors is because they are not as easily seen by our eyes. As a result, they often appear white.

All objects with a temperature above absolute zero radiate energy by emitting photons.
Most things emit photons you can't see: turn out the lights, you can't see them, because the photons being emitted are invisible to you.
As you increase the temperature, some of the highest energy photons will be emitted in the lowest-energy part of the spectrum you can see, which is the red and orange light.
Low temperature flames and a low-temperature metal element of your stove look like that.

Increase the temperature more, it emits more photons in the yellow-green region, the colour grows more yellow.
Increase temperature more, photons will be emitted about equally in all parts of the visible spectrum, so all colours of light are produced, and the light appears white.
White-hot is hotter than red-hot.

Increase temperature more, now very few released photons have so little energy that they are low-energy red, most are high-energy green, blue, violet, and even UV -- higher-energy than you can see.
That object will appear bright blue: blue-hot is hotter than white hot.

You see this progression with stars, and the colour of a star gives you an approximation of its surface temperature: red stars are <3500K, orange yellow white stars are progressively hotter, blue-white and then blue stars are around 8000K or more.

In theory, you can keep going.
Make the object so hot that none of the emitted photons is in the visible range, they start in the UV and go up from there.
The emitted light would be entirely invisible, or at best a pale violet.
In practice, that's not something you could ever actually do, because you'd need a temperature of like 50000K or more.

An oxy-acetylene torch will get you around 3800K, a plasma torch around 12000K.
Those flames are blue, and a plasma torch is about as hot as you're going to get outside a supernova.

Note that this all assumes that the colour is only due to the temperature you generate.
You can change the colour of a flame by throwing different chemicals into it, and the different elements will emit characteristic colours due to the energy levels of electrons in the ions, not the temperature.
You can make a low temperature blue flame by adding copper chloride, for example.