Based on – Specifies the source channel used to determine the smoke color. By default, a uniform simple color set by the Constant Color option is used. This could also be a texture map, or read from the cache files - in that case the corresponding grid channel must be present in the cache files and remapped to the internal Volume Grid channels using the 3rd Party Channels Mapping dialog in the Input roll-out.

Disabled - Smoke color is not rendered.
Temperature - Smoke color is based on the values of the Temperature cache channel and can be remapped using the color gradient.
Smoke - Smoke color is based on the values of the Smoke cache channel and can be remapped using the color gradient.
Speed - Smoke color is based on the values of the Speed cache channel and can be remapped using the color gradient. See the Smoke Color by Speed example below.
Texture - Smoke color is based on the values of a texture map plugged into the Texture slot.
Constant Color - Smoke color is the same for the entire volume and is taken from the Constant Color box.
RGB - Smoke is based on the values of the RGB channel.
Fuel - Smoke is based on the values of the Fuel channel and can be remapped using the color gradient.

Smoke Color Texture – If Based on is set to Texture, this slot specifies which texture to use.

Modulate by Texture – When Based on is not set to Texture, the color is multiplied by the texture in the Texture slot.

Constant Color – If Based on is set to Constant color, this color is used. 

Scattering – Controls how the light rays are scattered inside the volume.

Ray-traced (GI only) – Enables physically accurate scattering of light rays. This mode produces the most realistic results but it's the slowest to render. It requires V-Ray with enabled Global Illumination, otherwise, the rendered result would be the same as if the option is Disabled. The Master Multiplier does not affect the rendering in this mode.
Disabled – Disables scattering. The Master Multiplier value can be used to correct the brightness because without light scattering the volume would generally render darker.
Approximate – Uses an approximate formula which is faster than Ray-Traced scattering and produces good-looking results. Brighter areas of the volume would transfer light farther than dark areas. This option is not supported by the Volumetric Geometry render mode in the Rendering tab.
Approximate+Shadows – Same as Approximate, but also affects the strength of shadows over the scene geometry. Approximate+Shadows is not supported by the Volumetric Geometry render mode in the Rendering tab.

Scatter Depth – Specifies the maximum depth of the GI rays.

Volume Light Cache – Enables light caching for each voxel of the grid, which speeds up bucket rendering considerably when the voxel size of the grid is significantly larger than the rendering pixel. If the grid resolution is large enough compared to the rendering resolution, disabling this option speeds up rendering.

Light Cache Speedup – Valid only when Volume Light Cache is enabled. The higher this option is set, the faster the rendering will be, but the lower the quality of the volumetric Light Cache. You can increase this parameter and gain render speed as long as you don't start getting dark cubic grid artifacts on the smoke.

Own Light Scatter Mult – Valid only when Scattering is set to Approximate or Approximate+Shadows. This multiplier determines how far the light travels through the volumetric, based on the distance from the emissive light itself.

External Scatter Mult – Valid only when Scattering is set to Approximate or Approximate+Shadows. This multiplier determines how far the light from all external light sources travels through the volumetric. Both Scatter Boost parameters don't alter the visual density of the smoke to the camera and only apply to the illumination.

Master Multiplier – A general multiplier for the diffuse color. It is ignored when the Scattering mode is set to Ray-traced (GI only).

Shadow Strength – A multiplier for the opacity of the shadow that the volumetric casts on other objects.

The Smoke Color can be based on any channel present in the cache files. The Speed channel can be used to drive the color of the smoke. It is automatically generated by V-Ray Volume Grid based on the Velocity Grid Channel. In this example, the slowly moving smoke is blue while the fast moving smoke is red to yellow.

Smoke Color gradient – When the Based on option is set to a grid channel, this color gradient remaps grid simulation data to render smoke color.

This sim data has different ranges, depending on the solver it came from - Phoenix Smoke usually goes from 0-1; Fuel goes from 0-1; Temperature is in Kelvins, so it goes from 300-2000, or a few thousand; Speed is in Voxels/sec, so it depends on the grid size and resolution, but usually goes from 0 to several hundred. Data from other solvers often differs a lot from Phoenix ranges. The cоlor gradients in Cinema 4D are using 0 to 1 range. When the sim data goes outside the 0 to 1 range,the gradient needs to be remapped through the Gradient Min and Gradient Max values in order to match the grid channel range. You can find the exact range of your grid channels in the Frame Info tab.

Gradient Min – Remaps the minimum value used for the Gradient.

Gradient Max – Remaps the maximum value used for the Gradient.