Are all radishes hot?
Also question is, why are some radishes hot and others not?
The spiciness is caused by sulfur compounds in the radish. The amount and type of compounds depends both on the variety of radish (there are hundreds of them available in seed catalogs, many of which look similar) and the conditions they were grown under (soil, temperature, rainfall, drainage, fertilizer, etc etc etc.)
Then, how do radishes get hot?
According to Wikipedia, the flavor is "caused by glucosinolates and the enzyme myrosinase, which combine when chewed to form allyl isothiocyanates, also present in mustard, horseradish, and wasabi." Another factor that can affect the piquantness of radishes is their size.
While a traditional radish (the small red variety you usually find in salad bars) tastes spicy and peppery, the watermelon radish is a bit more mild. It still has a peppery bite, but it's much more mild than most radishes.