Pentium MMX has no thermal sensor. DIY.

Quite difficult since it's a pc cheap motherboard and there isn't a temperature sensor under the socket.
Few socket7 motheboard had the temperature sensor.

You can do it with arduino 😀 simple sketch reading thermistor and sending data over serial.

Standard DOS CPU usage is constant full usage AFAIK. Meaning it's not gonna vary with application/game load as they don't typically issue idling instructions (there is a TSR that can modify that though). In this case I assume you just want to make sure the CPU is doing fine with your cooling solution? So, what are you using? Pentium MMX requires a small heat-sink and a fan IIRC.

Thermal thermometer is one way to check.

Use DOSIDLE program to "stop" the CPU while doing nothing (issues HALT instruction).

Thanks everyone, great suggestions.

While we're at it, is it really safe to directly turn of the computer, when the hdd is running under MS-DOS? I mean, no safe shutdown way for the sake of HDD health?

Unless it's a REALLY old HDD, it should auto-park its heads on power-down. So I don't think it would matter.
This old thread discusses it: Hard drive parking.

Just turn off the machine outside of HDD activity to avoid bad FAT records. No need for anything else.