The issues involved with encaustic on paper are similar to the concerns of canvas. Supporting the paper is necessary and it needs to be prepared for display beforehand otherwise it the will fail as a substrate. This can be as simple as attaching paper hinges to as complex as sewing velcro onto the top edge of the paper. The major differences between paper and canvas is, that unlike paper, canvas is made up of fibres that are woven and will move and flex. The fibres of paper, however, are fused together, giving more stability and rigidity. This rigidity doesn't mean that paper isn't susceptible to the same effects of canvas, only differently and varying degrees.
Lets talk about SLAG: Slag is when gravity takes hold of your work pulling down on it; think about the way a sheet looks thrown up over a window. Over time slag will occur and how much will depend on how good you prepared your piece. There are a couple of sure-fire ways to prevent slag when using watercolor paper. One is how it is mounted and the second is using the proper paper weight (and by weight, I mean thickness, not how much the paper actually weighs).
Lightweight paper weighs typically around 90 lb, and heavyweight paper typically 300 lb or greater. Lightweight paper is ideal for collage or embedding; however, not for supporting an entire painting. For greater stability choose a heavyweight paper, 300 lb or more. The paper's weight is the weight measured in pounds of one ream, approximately 500 - 22" × 30" (Imperial) Sheets. However, you might come across paper measured using the metric system, grams per square meter (gsm). For example a standard sheet of 140 lb watercolor paper has a metric weight of about 300 gsm; usually the the seller will translate. In addition to weight, and as seen in the above picture, watercolor paper comes in varying degrees of texture; a preferential choice. However, neither are without their problems, rough papers are more difficult to mount and cold press (smooth) papers tend to curl.
Lastly, applying encaustic over a watercolor painting is another addition to using watercolor paper. There should be no additional issues involved unless acrylic based media was used or thick layers of WC paint are on the surface (e.g. do not use watercolor paintings that were done straight from the tube- simply stick with thin layers and watercolor washes).