If our Sun was a part of a Binary Star System, would it be too hot to live on Earth ? With two Suns, would we get double the heat from them ,than from our Sun alone ?
If another star with the brightness or lumminosity of the Sun orbited only 5 to 10 million miles from the Sun, and Earth orbited around both of those stars at the same distance as it orbits, Earth's goose would be cooked, as the saying goes, by the additional heat.
But the question doesn't specify where the other star would orbit or how luminous it would be.
the habitability of a binary star system depends on the distances between the two stars, the distance between the planet and each of the stars, and the luminosity of the stars.
The most massive stars are thousands of times as massive as the least massive stars. And the most luminous (brightest) stars are millions of times as luminous as the least luminous stars.
The circumstellar habitable zone is the range of distances from the star where any planets would be likely to have surface temperatures where water could be liquid instead of gaseous or solid.
Obviously the circumstellar habitable zone of a very luminous star would be many times wider and farther from the star than the circumstellar habitable zone of a very dim star.
Astronomers have now discovered several thousand exoplanets orbiting other stars, and some of them orbit within the circumstellar habitable zones of those stars and might possibly be habitable.
As for double star systems, there are three types of orbits possible for planets in double star systems.
A planet could orbit one of the stars, with the other star being farther away, which is called an S-type orbit or satellite type orbit.
Or a planet could orbit both of the stars, orbiting much farther from the stars than the distances between them, which is called a circumbinary orbit or P-Type orbit or planet type orbit.
Or a planet could orbit "librating" around one of the L4 or L5 Lagrange points relative to the two stars, in a L-type orbit or Librator type orbit.
I don't know whether there are any planets in L-type orbits in binary star systems.
But a number of exoplanets have been discovered in S-type orbits around one of the stars in a binary system, and a number of exoplanets have been discovered in P-type orbits orbiting both of the stars.
The masses and distances between the two stars in a binary system will determine whether S-type, P-type, or both types of orbits are possible and stable in that system, and the dimensions of the zone or zones where stable planetary orbits can be.
And the luminosities and distances between the two stars in a binary system will determine the inner and outer edges of any circumstellar or circuminary habitable zones there may be in that system.
If a zone of stable orbits and a habitable zone overlap, any planets orbiting within the space where they overlap can have suitable temperatures and potentially be habitable.
For example, the masses, luminosities, and distance between Alpha Centauri A and Alpha Centauri B make it possible for planets to have stable S-type orbits in both the circumstellar habitable zone of Alpha Centauri A and Alpha Centauri B. And there are unconfirmed reports of planets orbiting Alpha Centauri A and B which might be confirmed some time in the future.
In the 40 Eridani system each of the three stars could have planets in stable orbits around it, and there is one known planet orbiting 40 Eridani A.
So there are probably a lot of double stars which can have planets in stable orbits in their habitable zones with temperatures suitable for Earth life forms.