I have no experience embossing white birch. Temperature has nothing to do with the depth of the profile, this is determined by the design of the die or wheel. The light scorch left by the die also enhances the design by providig an even shadow along the design. I know that aspen, birch and soft maple have all been quite widely used for embossing on furniture in Europe, using high-temp rollers and platens. Poplar is a very common wood for embossing.
Many embossing companies run quite a variety of woods.
I have some cherry, soft maple, birch, and mahogony that has been embossed at a company I recently visited. The type of wheels and embossing machine, as well as the amount of detail in the profile, can limit the wood species that work the best. The depth of the embossing profile, at least from my experience, is affected more by the temperature control on the embossing wheel than about anything else. The feed rate of the embossing machine must be set to allow the embossing wheel to maintain the proper temperature. E-mail us and let us know what you think.