Supplementing what's already been noted, the material you see is a potting compound. It is not melting, but is slowly breaking down and oozing out. Potting compound has been used for decades in electronics to seal for environmental protection against moisture, debris, etc. and movement of internal components from vibration, mechanical shock, etc. The compounds are typically fast curing two part or single component chemicals that form a solid or semi-solid protective barrier. Over time the compound can break down and "run" or otherwise deteriorate. Heat does not necessarily cause it, but can aggravate the breakdown.
Chrysler used semi-solid potting compounds in the electronic control units (ECUs), electronic voltage regulators, air conditioning high speed cutout controllers, EGR timers, and other similar electronic modules. In some ECUs and voltage regulators, sand was added to the compound as an additional stiffener for mechanical shock and vibration resistance.
1970s assemblies are more susceptible to the oozing than later production parts. Later production was changed to a more rubber-like or silicone-like compound that breaks down less. In general, the parts can continue to function with the compound leaking out unless affected by moisture or other factors. Aftermarket components can also suffer from similar breakdown depending on the nature of their compound.
When the early compound used by Chrysler oozes it forms a sticky mess. It can be dissolved with lacquer thinner, but it's tricky to remove from painted surfaces without risking the paint. I've successfully removed it with lacquer thinner from vehicles as well as ECUs and voltage regulators, including the internal areas. Removal from the internal areas does risk removing electronic component markings and weakening the components, especially the electrolytic capacitors. I have replaced the removed potting compound with two part (A-B) silicone or urethane compounds.
ECU replacement is not necessary due to the oozing, but when the internal components are uncovered, they could be affected by the environment. The ECU can continue to work though and not necessarily electrically fail due to the oozing.
In 50+ years of working with Mopars, I've only seen a couple or so of real ECU electrical failures on our own personal vehicles and maybe only two or three ballast resistor failures (all 4-pin). One single ballast resistor failure too, but that was an original resistor on a point system (1966 Belvedere 318 Poly in the late 80s). One ECU was the original that failed after 46 years. Almost none of the potting was left in it, but I have not looked further yet to see why it actually failed. Another was a Chrysler ECU with a "Mopar Remanufactured" sticker on it that came on my 1974 truck that I got in 1990. It failed about 10 years later. I have a Borg Warner ECU that is flaky. It works, but fires oddly, and triggers the coil without the engine running, but key on in "run".
Replacements of my own vehicle ECUs have mostly been due to potting issues, a "better" ECU, or a preferred different ECU, not functional failures. For potting issues, I re-work them to clean it up.
Here is an ECU that oozed on my Duster with bugs and other debris stuck in it and after cleaning the oozed potting off the car and re-potting the ECU:
I've done others. Cleanup difficulty varies depending on the extent and the mounting.
These are my ECU spares and some being re-worked for potting compound breakdown and oozing.
These all work, both Chrysler and aftermarket. Some I bought new years ago, some NOS later, some are used original Chrysler, and others are new aftermarket. None are newer manufacture than the mid 90s, so none are the newer cheap, inferior offerings without proper internal components. Several brands are here: Chrysler, Chrysler Direct Connection, Wells, Sorensen, Filko, Kem, Big A, Echlin, Standard/Elextron, Auto-Tune, Atlas, and Motorola.
These two ECUs were removed from cars in a field. Both are originals that Chrysler installed in the cars. One in 1974, the other in 1976. They both still work but will be cleaned up and re-potted.
These have had the potting removed.
The "de-potted" ECUs have been re-painted and tested, but not re-potted yet. I don't attempt to make them look original, just somewhat decently so. I might replace a sticker.
In addition to these, each of my 15 operating vehicles have Chrysler factory electronic ignition as installed, or added by me with other factory parts or Direct Connection/Mopar Performance kits. Each of those also carry a spare ECU in the trunk, although I've never had to use one on the road.
I can repair the ECU if needed depending on the fault, but removing the circuit board from the soldered connector pins and the main power transistor is a hassle. I've broken a capacitor in the potting removal and had to correct that. Actually, in 50+ years of working with Mopars, I've only seen a couple or so of real ECU failures on our own personal vehicles and maybe only two or three ballast resistor failures (all 4-pin). One single ballast resistor failure too, but that was an original resistor on a point system (1966 Belvedere 318 Poly in the late 80s). One ECU was the original that failed after 46 years. Almost none of the potting was left in it. Another was a Chrysler ECU with a "Mopar Remanufactured" sticker on it that came on my 1974 truck that I got in 1990. It failed about 10 years later. I have a Borg Warner ECU that is flaky. It works, but fires oddly, and triggers the coil without the engine running, but key on in "run". I've had two that were intermittent, one Direct Connection, and one Atlas. Replacements have mainly been due to potting issues, a "better" ECU, or a preferred different ECU. So, I have more spares than I likely will need, but if I see a good deal on a good NOS unit, I am tempted to grab it.
I can test an ECU or factory wiring with the factory tester. It's typically easier and more realistic though to just temporarily mount the ECU on a vehicle and start/run it for testing. For checking ECU wiring checking, I prefer a multimeter.
I converted one of my failed ECUs into a wiring junction box for experimenting with a semi-hidden MSD-6A with a stock electronic distributor to appear factory and to allow me to convert back to a stock ECU without re-wiring if needed. I saw no real benefit with the MSD other than maybe tolerating wider plug gaps better, so I removed it for stock. I experimented similarly with a Jacobs Ignition setup which showed more benefit, but I later went back to stock on that one too.
I'm doing similar rework on 1970+ voltage regulators and police air conditioning cutouts which can also suffer from potting breakdown and oozing.
FYI...