As noted by @a4android in the comments, a hypothetical Earth in a Mars-like orbit probably would have developed much differently (especially with respect to biological activity). I don’t think that’s what you’re curious about, so in this answer I’ll consider what would happen if modern Earth was transplanted into Mars’ orbit.
The sun emits radiation radially outward, and we can imagine a spherical “shell” of radiation emitted at any particular moment inflating with the sun at its center. At a distance $R$, the radiation emitted from the sun is distributed over a sphere with surface area $4\pi R^2$. Since the same amount of radiation is spread over a greater and greater area as it moves away from the sun, intensity decreases proportionally to $1/R^2$. Therefore, since moving Earth into Mars’ orbit increases its distance from the sun by a factor of about $1.4$, the intensity of sunlight striking its surface is multiplied by a factor of $1/1.4^2\approx 0.51$.
If $T$ represents temperature in Kelvin, then light intensity is proportional to $T^4$, meaning that multiplying intensity by $0.51$ results in $T$ being multiplied by $(0.51)^{1/4}\approx 0.85$. 921
Thus, the immediate result of the distance increase will be an approximate $15\%$ decrease in average surface temperature.
However, it will actually be a lot more severe than that, because of two self-reinforcing climatological cooling loops:
* Snow (often) has a high albedo. Regions that receive more snow as a result of cooling will also reflect more of the sun’s radiation energy. This means that the overall proportion of solar energy absorbed decreases, causing greater overall cooling.
* Water is a greenhouse gas. At lower temperatures, more water will be liquid or solid. This means less water in the atmosphere to help trap heat, causing even greater planetary cooling.
This will probably end up being much more harsh than you were hoping. If so, you might consider either increasing the sun’s luminosity (if distance from the sun is crucial in your alternate reality) or putting Earth a bit closer (if a slight but manageable decrease in global temperature is what you’re after). 184