I agree that normal room temperature should be OK. I also agree that significant temperature fluctuations can be detrimental, even to the point of killing the plant, depending upon the species and the temperature differences.
On the light, be careful of direct sunlight. This can cause problem algae. Controlling natural sunlight which can vary from day to day, season to season, in terms of the intensity and the duration, is more difficult than contolling artificial tank lighting. I found this out when I ran anexperiment with a planted 10g in front of a window as the only light source. The plants grew well, but algae and even cyanobacteria appeared.
Re the actual plant...Anacharis is a "common" name for the species Egeria densa. [However, there are sources where this is confused and Anacharis is there considered synonymous with Elodea nuttallii. It might help if we never used the incorrect name Anacharis whatever it may refer to.] This plant prefers cooler temperatures than what is found in the normal community tropical aquarium, and frequently will fall apart within a few weeks if kept at warmer temperatures. A closely-related species, Egeria najas, does very well in normal temperatures (optimum 15-26C/60-79F) but is rarely available (Kasselmann, 2003).