A star hot enough to be orange wouldn't actually be a red dwarf? Such a star would be a K type star, whereas red dwarfs are type M. There are supergiant stars of this class, but the regular variety you'd be interested in would be around 0.45 to 0.8 solar masses and would really just be a slightly cooler version of our own Sun (G type). In fact, this type of star is the one that scientists looking for extra-solar life are most interested in, because they are longer lived than G type stars, emit less harmful UV radiation, and don't have the problems M type stars do where the habitable zone is so close in that any planet in it would almost certainly be tidally locked.

A typical K type star would have a surface temperature of 4500K (compared to 6000K for our Sun), a radius 0.8 times Sol, and about 0.2 times its radiation output. Given such a star, and bearing in mind the inverse square law, you'd expect a similar level of radiation to reach an Earthlike planet at a distance of 41 million miles. Orbital period would be approximately four Earthly months. The star would appear rather larger in the sky than the Sun does for us because you're so much closer in, even though the star itself is smaller.