in my experience, a single male paradise fish is pretty calm in a big tank like a 60g but terribly aggressive in a small tank like a 10g. most people who have tried keeping them in communities under 20 gallons have had serious aggression problems. think of them as being like overgrown bettas: irritable, territorial, and not to be kept with other paradise fish.
as for the tank needs of an individual, 5g at the absolute minimum and 10g preferably. an adult male paradise fish will have a 3.5" long body with another 1.5" of tail. paradise fish are pretty deep-bodied fish, so the typical inch-per-gallon is really an underestimate here. however, if you keep only the one paradise fish in a heavily planted tank, then you probably could get away without a filter. a heater is 100% optional in either case. if you're happy sitting around in a t-shirt and jeans, then that temperature is just fine.
FYI: paradise fish love algae wafers and flakes. feeding them spirulina is a great way to enhance their color and really make your paradise fish happy.