I'd put an active h/s (one with a fan) and retry.

Post pics in high res when possible.

I dove into the reference guide for the TI486-series for a bit. The TI486DLC/E-40GA is specified for a maximum supply current of 700 mA (page 5-9, 206). For comparison, a 40 MHz Am386DX is specified to draw a maximum of 400 mA (page 105).

Sadly, I don't have the proper tools to check the current draw of the CPU or motherboard, so I thought I'd do some checking via the thermodynamics side of it instead.

I'm assuming the current the CPU sources on its I/O pins to be negligible and everything to be dissipated inside the CPU package, resulting in the CPU having to dissipate 0,7A × 5V = 3,5 Watt. In addition I'm assuming the CPU to be made entirely from material which has a heat capacity similar to sand, being c = 0,835 J/(g × K), and guesstimating to have mass m = 15 grams.

Seeing as c = Q ÷ (m × ΔT), with Q = 3,5 Watt = 3,5 J/s, this would then result in temperature change ΔT = 3,5 ÷ 0,835 ÷ 15 = 0,28 K/s. Assuming a room temperature of 23 ℃, an "uncomfortably hot" temperature of 50 ℃ and discounting any heat loss to the outside, the CPU would become uncomfortably hot in time t = (50 - 23) ÷ 0,28 = 96 seconds.

So if my impromptu math is correct, a TI486DLC getting this hot is probably entirely normal.

Edit: typo's.

If it's consistently a few programs giving you crashes, you can flip the L1 on and off to see if it makes a difference https://www.philscomputerlab.com/cyrix-486dlc.html

Otherwise, you can't really go wrong in keeping a CPU cool, passive cooling solutions do have to generate a bit of delta T before convection really gets moving.

As long as you have 4MB+ RAM, Doom is a quite reliable stability test up to PIII/K7 class, loop the demo for a bit.

Yeah it does get toasty in there. I had to install a heatsink and fan on mine just for peace of mind. However, crashes might not be heat related. There was another thread a while ago where we discussed different 486DLC tweaks and issues with L2 cache chips not being up to snuff.

I've added a heatsink + fan combo to the CPU (which has the added bonus of providing some airflow over the math coprocessor and memory as well), and I've yet to see another crash.

As requested, I've attached some high-resolution pictures for future reference. As you can see this board was plagued by the infamous leaky Varta problem; I've actually had to desolder, clean out and resolder the keyboard connector to get everything cleaned. Luckily the rest of the board wasn't affected.