I will address the direct impact of a supernova on the Earth's temperature, ignoring secondary effects like effects on cloud formation which may also be important.
Let's assume that a supernova's direct contribution to Earth's heat budget is entirely due to electromagnetic radiation emitted during the supernova (we'll ignore neutrino emissions which are poorly absorbed by the Earth and energy carried by stellar material, which will take a long time to reach the Earth, if ever).
Let's assume that in order to have an appreciable impact on the Earth's temperature, the energy of the absorbed incoming radiation must be comparable to the amount of radiation absorbed from the Sun in a day.
Let's furthermore assume for simplicity that all EM radiation from the supernova that is incident on the Earth's surface is absorbed.
Let $d$ be the distance to the supernova, $\sigma_P$ be the incoming power density from the sun, $E^{emit}{nova}$ be the total emitted EM energy of the supernova, $R_E$ be the Earth's radius, $T$ be the length of a day, $E{\odot}$ be the daily incident solar energy, and $E^{inc}_{nova}$ be the total incident energy from the supernova.
$$E_{\odot} = \sigma_P \pi R_E^2T$$
and
$$E_{nova} = E^{emit}_{nova} \frac{\pi R_E^2}{\frac{4}{3} \pi d^2}$$
Given a incoming EM power from the Sun of roughly $1400~W/m^2$, this gives us
$$E_{\odot} = 1.5\cdot10^{22}~J$$
According to the references in this wikipedia article, the upper limit on radiated EM energy from a supernova is $0.1~foe$, or $10^{43}~J$. Let's start with Alpha Centauri going nova, at a distance of $4.3~ly$:
$$E_{nova} = 1.8\cdot10^{23} J$$
Thus at an upper limit, we could expect roughly 10 times the daily thermal input from the sun to come in a short period of time from Alpha Centauri's demise. It's safe to say this would be not just significant, but devastating to life on Earth.
So where is the break-even distance, where a supernova would provide a heat input comparable to one day's input from the sun? Setting the right hand side of the above equations equal to each other, we arrive at
$$d = \sqrt{\frac{3E^{emit}_{nova}}{4 \sigma_P \pi T}}$$
Which for our values yields $d = 14.8~ly$. Given the inverse square scaling of the incident energy, I conclude that incident radiation from supernovas that are an order of magnitude further away than this, say greater than $100~ly$ away, should have at most a transient impact on the Earth's temperature. 912