Yes, mars is too small to hold its atmosphere at its current distance from the sun, moving it closer would only make the problem worse. Like our moon, the bright side would be hot during the day, but it would be cold at night with very little atmosphere to retain heat, and even in temperate regions at the poles liquid water would not be stable.

We're not really sure what kicked off Venus' runaway greenhouse, so it's possible that would still occur, though it does seem less likely. Without the runaway greenhouse, Venus' atmosphere would likely remain primarily nitrogen. Its atmosphere would still be significantly thicker than Earth's but by a factor of 5 instead of a factor of 100. With the additional atmosphere, it might remain quite temperate even at the greater distance.

Of course had Venus and Mars developed in eachother's places, Venus would have developed as a smaller world with a thinner atmosphere (generally more mars-like) and Mars would have been larger with a thicker atmosphere (generally more venus-like), so the whole point is somewhat moot.