Some motherboards have utilities provided by the manufacturer that can run under Windows. Tyan, for example, has a monitoring utility that supports a bunch of their motherboards.
What brand/model of motherboard is it? That might help somebody think of an alternate tool. A manufacturer provided tool is probably the most likely to interpret the sensor values the way they intended.

Speedfan typically detects a whole bunch of sensors, some of which are not really valid. It's possible it just needs to have different sensors enabled. I think it also has some way to add offsets to the readings. But of course in order to do that you'll need to find some more trusted readings inside Windows to compare with.

For voltages - motherboard sensors aren't really trustworthy. I would check them with a multimeter to see what the voltages really are. I've seen several boards where the voltage sensors were way off from reality. The easiest voltages to check are the +5V and +12V, which are on the 4pin molex drive connectors.
The onboard sensors are still useful though just for noticing whether the values are changing, even if their absolute reading might not be accurate.

The same inaccuracy is probably true for the temperature sensors, but it's not as easy to get a true reading of the temperature so you're more forced to trust what it says.

Motherboard is asus A8V deluxe. I previously checked the 5V and 12V with multimeter and there was only difference of 0.02-0.04V between what multimeter showed and what bios shows.
Bios cpu temperature was 5-7C higher than highest temperature that speedfan showed and the temperature must have dropped few degrees before I got into bios when it was restarting.
I assumed already that cpu temp wasn't the temperature that speedfan said was "core" temp because it was "Temp 2" value that started rising in speedfan when I started the stress test in prime95.

I did dig up my old original cd that came with the motherboard. There is Asus pc probe software that seems to get mostly correct values except 12V voltage shows 11.64V when multimeter and bios show about 12.25V. It could be very old version of the software though, so I will try to check online if there are any newer versions that work with win98se.