Some plastics, such as 6/6 nylon, are so resistant to abrasion that it is very difficult to machine them, but have very low viscosity once melted. You can cut nylon with an abrasive wheel, for example, but it destroys the wheel. Acetal (that is, polyoxymethylene or POM, aka Delrin) is popular not primarily because of its material properties — although they are quite good — but because it can be cut much more easily than most other thermoplastics.
Plastic foams such as Styrofoam can be cut using a hot wire, typically stainless steel, but this approach doesn’t work for solid plastics; the molten plastic closes up the kerf behind the wire. Hot-wire cutting also typically suffers from poor temperature control, vaporizing and burning some of the plastic, which increases the risk of hazardous fumes.
Suppose that instead you had a narrow steel or aluminum pipe, for example 8 mm diameter with 0.5-mm-thick walls, heated to a precisely controlled temperature by pumping heated oil through it. The oil could, for example, be heated to 290° and pumped around a closed loop past an electrically heated aluminum heatsink, with the heat applied to the heatsink controlled by a thermostat measuring the temperature of the output oil. With this approach, most of the molten nylon can be made to run out of the kerf as the pipe advances through it, particularly if the nylon material is in a sheet of only a few millimeters thickness.
If we take 45–45 cal/g (188 kJ/kg) to be the heat of fusion — a bit less than that of paraffin — 271° to be the final melting point, and 1.21 g/cc to be the density of 6/6 nylon, from Starkweather, Noller, and Jones 1984 then melting a 9 mm kerf through a 20 mm thickness of nylon would require 41 J/mm to do just the melting. If we believe Engineering Toolbox’s specific heat table, the heat capacity is 1.7 kJ/kg/K, so heating by 250 K is another 425 kJ/kg, for a total of 613 kJ/kg. This means that same 9 mm kerf at 20 mm thickness requires 135 J/mm. So cutting at a reasonable speed of 10 mm/s, neglecting conduction, requires 1300 W. Cutting at higher powers is more efficient, because you'll get a smaller error from neglecting conduction.
Polyvinyl chloride is another example of a plastic that can be easily cut with a hot object, but is hazardous with poor temperature control. If we believe the Polymer Science Learning Center’s decomposition temperature table, PVC decomposes in the 200°–300° range but doesn’t melt until 265°, and nylon 6,6 decomposes in the 310°–380° range, while PET melts at 268° and decomposes in the 283°–306° range.
Transferring 1500 W to oil through a heatsink probably requires a heatsink of some 100 mℓ capacity, so the total amount of oil needed for this tool is probably around 150 mℓ.
Avocado oil has a smoke point of 270°, which is probably high enough to melt nylon, but more normal cooking oils like soybean oil smoke at much lower temperatures like 238°. This suggests that if a nontoxic oil is to be used in this tool, it has to be medical-grade paraffin or polydimethylsiloxane rather than any actually edible oil. I’m not certain that either of these, but especially medical-grade paraffin, will withstand such high temperatures; Engineering Toolbox suggests a limit of 149° for mineral oil and 260° for PDMS or other silicones, but I suspect that may just be the point where the oil ceases to lubricate. Some companies do sell high-temperature lubricants capable of lubricant use up to 270° and more; the fluorinated Krytox XHT supposedly doesn’t degrade until 350° and doesn't corrode metals until 288°.
If the oil is heated to 290° and must not cool below 271°, we only have 19 K of sensible heat in which to store all the heat to be delivered to the nylon. If the oil has a heat capacity of 1.67 kJ/kg/K (according to Engineering Toolbox's table), that's only 32 kJ/kg, so we need 47 g/s of flow. At 0.8 g/cc, that’s 59 mℓ/s. If a single-acting piston pump driven at 1500 rpm is driving this, the pump’s displacement needs to be 2.35 cc.
In a 7-mm-diameter pipe, that’s a rather shocking 1.5 m/s average linear speed. The Reynolds number is almost 11000. But according to an anonymous online calculator, the pressure drop from 200 mm of such a flow with .01 mm pipe roughness, if the fluid were water, would be only 11 mbar (1.1 kPa). This implies that only 65 mW of pumping power is needed, which seems surprisingly small to me, suggesting that maybe my pipe resistance calculation is wrong. Another random online calculator suggests that the head loss will be 294 mm, which would be 2.9 kPa, which is a little higher but still in the ballpark.
These high powers suggest that it might be desirable to power the tool directly with fire rather than electrically.
Alternative heat transfer fluids might include perfluorocarbons (like the Krytox XHT mentioned earlier), molten salts, and molten metals.
In particular, ordinary tin-lead 63/37 solder melts at 183°, doesn’t boil until 1500°, and doesn’t suffer chemical breakdown.
It does tend to dissolve metals — tin quite rapidly, of course, but also gold, silver, and copper at significant speeds, and even nickel some 25 times slower than copper. In the case of copper, the dissolution diminishes rapidly once the solder is saturated with dissolved copper (at a fairly low level), as is done in SAVBIT solder. Presumably this also applies to other metals it can dissolve, too. People add nickel to solder to keep it from dissolving iron. Phosphorus counteracts this effect and increases stainless steel erosion — in lead-free tin-copper solder.
There’s debate about whether tin-lead solder is capable of even joining steel, which I thought might imply that it has a very hard time dissolving steel as well. Other alloys (lead-silver, cadmium- silver, tin-silver, and maybe tin-bismuth) supposedly work well for joining steel. But apparently tin-lead solder does work with steel if you use acid flux.
Molten solder in wave-soldering equipment is normally contained in stainless-steel equipment, which suffers erosion over a period of months, but this is at lower temperatures than what I'm discussing here. One study I found, though, found about 0.25 mm erosion depth on stainless steel 304 (and a bit less on 316) after 384 hours in a 350° lead-free solder, which seems slow enough that the tool could still be useful.
Type metal is a variant that has the desirable property that it doesn’t have a sudden change in volume when it melts. It's a tin-lead solder that also includes antimony; the traditional composition is 18% tin, 28% antimony, 54% lead, while the eutectic is 4% tin, 12% antimony, 84% lead, which melts at 240°. (Elemental antimony is fairly nontoxic, although its compounds are deadly, and its fumes are bad for you too.) Legend has it that type metal is very poor at dissolving iron.
Scrap type metal from Linotypes and the like is available on MercadoLibre at AR$55/kg (US$3.60/kg).
If using a coolant that melts above room temperature, then to keep the machine from freezing solid permanently the first time you turn it off, you could thread a resistance heating element all the way through the pipe, probably with insulation around it. That way, when you turn the element on, it will melt a path around it through the tube, allowing the coolant to begin to flow.