If two hot resistors are touching each other, will their temperature rise as opposed to not touching?
As the long string of comment debates suggests, bringing the two resistors will cause their temperature to rise.  This will not happen because the resistors are making each other hotter, but rather because you will limit the amount of cooling available.

In both scenarios we assume that the resistors are being cooled by convection.  The resistors are heating the air around them and that is causing the air to rise away.  This may also be forced convection, where we have a fan pushing the air across the resistors.  Regardless of the reason for the air movement, the important fact is that we have air moving past the resistors to cool them.  Anything which decreases this cooling effect will cause the resistors to get warmer.

If you were operating this circuit in a vacuum, the story would be different.  Without air, there would be no convection.  Without the cooling effects of convection, there would be no change in temperature by bringing the two resistors together.

Incidentally, designing circuitry to work in vacuums is very difficult due to heating issues.  Because there is no convection, you have to consciously design your circuit to include direct paths to sink heat way from your chips.  Poorly designed circuits have been known to get hot enough to melt the solder and let the chip fall off of the board.