Nerf the RR by widening its hipfire by about 200%. Buff its optimal range by 10 meters, up to 90.
Nerf the CR by adding a 0.05 second delay between bursts, and make it kick slightly more than other rifles. This will allow exactly 5 bursts per second, or 480 max DPS down from 640 DPS.
Nerf the ScR by reducing it RoF from 705 to 570. This will allow 9.5 shots per second, or 684 max DPS from 846 DPS
Nerf the ARs optimal range by 15 meters, down to 45. Buff its damage from 34 to 38. This will increase its DPS to 475 from 425.

Now we have this.

AR: Powerhouse in Close Quarters Combat. Ineffective at longer ranges.
CR: Powerhouse in Close-Mid Range Combat. Has more range than AR, but also has a smaller mag size and more kick.
ScR: Capable of great DPS and range. Overheat functions keep this weapon balanced.
RR. Has good DPS and great range. Unwieldy in close quarters combat.

This is a terrible idea... what justifies the AR to have 30 meters range just to have 11% more DPS. At this range and based on what the AR should do it should be doing DPS matching the SCR. Your suggestion turns the AR into a smg with the second lowest DPS and a range outclassed by 67%.

Keep the guns how they are, just nerf the DPS of longer ranged guns, placing the AR as the second highest DPS just next to the SCR, the CR as the third highest DPS and the RR as the lowest DPS.

I mean, part of what balances the Scrambler Rifle from being super OP is the fact that it stops firing after about 15-20 continuous shots. Why not apply this mechanic to the Rail Rifle too?

The reason this is a balancing factor is simply because of the range. If you've ever used a scrambler at long range, you'll know that cover is your best friend. If you accidentally overheat you have to retreat, which is much easier when you're in cover, than when you're face to face with the enemy.

However when you do engage an enemy at 10-15 meters and overheat, you have a massive disadvantage against a player using a short-range weapon that doesn't overheat.

The idea is that with an overheat mechanic, players would be less likely to spam the RR in CQC like they do now. With how hard it is for players to hit their target, chances are the RR user will most likely overheat before they can deal lethal damage. If they try and burst fire the weapon, they will be at a huge disadvantage against other weapons that are much more effective with burst firing thanks to the .25 second charge up time every time you let go of the trigger.

On top of this, the overheat will make the .25 second charge-up time feel much heavier. When you have to constantly stop firing to let your rifle cool down, you have to endure that charge up time every time you start firing again. It's either you endure the .25 second charge a few times, or you overheat your weapon and wait 5 seconds.

The best part is that at long ranges this hardly affects the weapon. As most of you know, the RR already kills most players in 3-6 shots, which means that unless you are a really bad shot, or if the player is at your max effective range, you won't ever overheat when you're using the weapon as it is designed.

After considering EVERY other option, this seems like the best way to add some balance to the weapon in a way that doesn't hamper its main ability to kill at optimal range, but decreases its effectiveness in the areas that it really shouldn't be so effective in.

Not 30m. 45m, the current AR has an Optimal of 60m. 60-15=45
For reference, the AR used to have a 45m optimal until it got buffed to 60m in 1.7, and even then it was considered OP.

AR: 45m, 475DPS, full auto
CR: 60m, 480DPS, burst fire
ScR: 75m?, 684 DPS, semiautomatic
RR: 90m, 423 DPS, full auto

Optimal range for the AR is 48...

I'm almost positive they buffed it in 1.7