Ok, the gotcha with the "direct to the supply" approach is the inability to take most of them to zero volts. That's one of the things you very much want to be able to do on a temperature controller.
Do we? A typical minimum voltage would be 1.25 V to 1.5 V. Say German_EE uses a 24 or 48 V supply because he isn't nuts and doesn't use some stupidly low voltage to heat things. A resistor powered by 24 V would dissipate only about ~0.3 % of that power at 1.25 V. In many applications the minimum outward heat flow will be much greater than that (You'd not use a heater that can go to 11 if all you needed was one that goes to 3, right?).
In terms of fire hazard / safety ... well, the heater needs a secondary shutdown mechanism anyway.
@Triacs and low voltage transformers: note that losses in the triac are _much_ higher relative to the delivered power compared to 230 V operation. If so I'd suggest _full_ wave control from the primary of the transformer. That way, you have much less power to dissipate.
Hi
With a switcher, without changing the output caps, you aren't going to get a 48V to 1V output range. The thing will go unstable. Once you start switching output caps and feedback parts, it gets really messy really fast.
There is no reason to do it. Simply do a PWM on the output of the regulator. Much easier, no nasty things to mess with.
My assumption on the tirac is that you simply have a 1:1 transformer on the thing to ground isolate the system. The triac will blow any switcher made away efficiency wise. It will hold efficiency to a much lower power level than a crazy switcher.
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Now, if he wants an oven that is precise, there's more to it. Gradients quickly become the dominant factor. You can have a 0.0000000001C set point and have 5C gradients at pretty normal temperatures. The answer is either a stirred liquid or a lot of moving air.
The pump or fan will put the whole discussion about "how efficient" (93 or 96%) in the waste basket.
So far there is not a lot of numbers behind this. How hot does it get? Does it start from a heated room? (My back porch is at -10C ...). How much heat load is there (if any)? What sort of uniformity is needed? The answers to those sort of questions could easily impact what needs to be done.
Bob