Noise isn't modeled.
All preamp tubes have separate heating elements. This is called "indirect heating". Directly heated cathodes are no longer used except for rectifier tubes. Regardless direct or indirect heating has no effect on the noise floor. Noise is due to the random motion of electrons in a conductor. You can't "reject" it. You can lower the noise floor by keeping resistor values low (since noise is proportional to resistance) and by paralleling the input triode.
No modeler models noise. The dominant source of noise in any amp, whether real or virtual, is usually your guitar (or rather its pickups). A 10K ohm pickup will have -114 dBv of noise at room temperature. Modern A/D converters, when properly designed, can exceed this so the dominant source of noise is your guitar. This noise is then amplified by the amp (that's why they call them amplifiers). If the amp has, say, 60 dB of gain then that noise is now -114 + 60 = -54 dBv. Gain it up another 20 dB with the power amp and now you're at -34 which can be quite audible.
The situation gets worse as you roll off the volume in your guitar as you then introduce more resistance. A typical guitar pot is 500K ohms with an audio taper. If you roll the volume pot down to 8 or so you can easily introduce another 100K of resistance into the signal path. This will increase the noise to -94 dBv which becomes -14 after amplification. Really noticeable then.
Bottom line: if you have too much noise you have too much gain. Learning to play with less gain will improve your technique and the quality of your tone. Gain just masks poor technique and reduces clarity, string separation and dynamics.