what effect the root growth of the plant?

Well for starters, roots grown against light since they are negatively phototropic..
The temperature really depends on the type of plant root we're talking about... some prefer to grown in the winter, and some in the warm temperatures
and for their media, they always need water and nutrients.. Metal nutrients in a usable ionic form is required such as ironsulphate. Nitrogen fixing bacteria are needed to be present in the soil so that Nitrogen could be fixed from the atmosphere into its absorbable form which is nitrate. Some fertilizers, manure, or compost would also enhance the growth. Oxygen and air spaces between the soil particles is crucial as well.
On a further notice, you might want to decrease competition by neighbouring plants if they were there to give the roots some space. Plants that are next to each other may fight for space by "poisoning" the soil around them with chemicals or acids that may be fatal or weakening to the plant nearby.

Hope this helps