No problem with the radiant heat. Acid stains are the most popular. They are U.V. stable and provide for a marbled look that can highlight cracks and other irregularities in your concrete. Many people like this look. Colors are limited to 8 tone selections.
Then there are water based and solvent (usually acetone) based dyes. The solvent dyes are more vibrant and the water based more soft. Both are available in a multitude of colors, they tend to create a more solid looking color, but they can fade over time if exposed to sunlight.
You can protect your floor with an acrylic sealer, which is the least expensive way to go - to an epoxy and polyurethane coating which is more expensive but provides for long wearing and very tough coating. A clear polyaspartic is another option.