I'm crunching on a laptop which doesn't have great airflow, so I wanted to underclock the GPU to avoid accidentally damaging the GPU, burning the house down, etc. I'm new to that and struggling to find instructions that don't presume everyone wants to overclock! So I wondered whether anyone who's done it before could check my understanding and perhaps offer advice.

I understand that the trade offs are:
High voltage -> Very high power draw and hence temperature.
High clock speed -> high power draw and temperature.
Low clock speed -> slower processing
Low voltage (for a given clock speed) -> instability and calculation errors.

I'll accept the slower processing, the bit I'm not clear on is the voltage and stability curve. I don't want to submit results 5% faster if half of them turn out to be wrong.
So how can I make sure that my chosen voltage/clock speed is going to be stable? Are there programs that will stress it in a more rigorous way than "play a game and look for artifacts?" Is it safe to just fix at a value on or below the default curve?

Thanks for any experience
Josiah

The short answer:
I would simply reduce the power limit in MSI afterburner until the temperature / noise reach the desired limit (you could use some similar GPU tweaking tool - however this one works fine with other brands also).

The TLDR part:
Overclocking and underclocking is the same thing with similar iteration of the ideal frequency / voltage combination, only their purpose is different (maximum performance vs maximum efficiency). So if you want to refine your underclocking further, then you can reduce manually the voltage and/or the GPU frequency with this tool. However I think that the GPUs have their own frequency / voltage and temperature / power consumption tables in their BIOS, so decreasing voltage will "automatically" decrease frequency to maintain the stability of the chip.
Regarding testing: You can pre-evaluate your settings by furmark or similar tools, but the only sure thing is the GPUGrid application itself. You should monitor the progress of your workunits closely, changing only one GPU parameter at a time, taking notes every time the time and date and of what you've changed and what else changed "automatically". As different workunit batches stress the GPU to different extent, one setting may not work for another batch, so if a new batch is failing, you should probably increase voltage, or more likely decrease frequency (just as when overclocking).
Note that power consumption is in square ratio with voltage, and in direct ratio with frequency. E.g. decreasing voltage by 10% without reducing the frequency saves more energy (21%) than decreasing frequency by 10% without reducing the voltage. As far as I know this two parameters are linked for stability reasons, therefore in practice you can't reduce one of them without the other being reduced automatically - the another consequence of this behavior is that you don't have to figure out that voltage vs stability curve as it is programmed into the BIOS.

Thank you.

It had not occurred to me to use GPUGrid itself to check for stability. I'll keep an eye on it.

I'm usually using 1, currently 2 GTX1060 in my PC. These have power limits of 120 and 140W. When running full throttle these produce far to much heat to be cooled silently (1 x 140mm exhaust vent being the bottleneck).
When I set both to a power limit of 70W, their boost clocks drop by 100-200MHz depending on the load (here GPU utilization by GPUGrid). I'm gladly trading that ~10% drop in MHz against an almost 75W reduction in power draw, heat output and hence fan noise.
It's as easy as that, just decrease the power limit. No need to further fiddle with frequencies and voltages. Nvidias Boost mechanism will get you the best clocks within the limits you allow.