Need to control (fade in/out, not just turn it on and off) a 240 V heat lamp. Is this even possible?
The power part of the solution is quite simple using a linear proportional controller. For example, this type of controller uses an analog 0-5V or 0-10V signal to control the switch-on time of a triac which feeds your load.



Figure 1. Linear proportional controller wiring.

The output of this will generate a variable AC power with waveform as shown in Figure 2.



Figure 2. Proportional control of AC power.

Link: Linear proportional controller.