STM32 ADC: leave it running at 'high' speed or switch it off as much as possible?

Question

I am using a G0 with one ADC and 8 channels. Works fine. I use 4 channels. One is temperature that is measured constantly and I am interested in the value every 60s. Another one is almost the opposite: it is measuring sound waves for a couple a minutes per day and I need those samples at 10kHz.

I solved this by letting all 4 channels sample at 10kHz and have the four readings moved to memory by DMA (array of length 4 with 1 measurement each). Every 60s I take the temperature and when I need the audio, I retrieve the audio values.

If I had two ADC's, I would start the temperature ADC reading for 1 conversion every 60s. Non-stop. And I would only start the audio ADC for the the couple of minutes a day that it is needed. But with the one ADC solution, it seems simple to let all conversions run at this high speed continuously and that raised my question: Is there any true downside in having 40.000 conversions per second, 24 hours per day? If not, the code is simple. I just have the most recent values in memory all the time. But maybe I ruin the chip? I use too much energy I know. But there is plenty of it in this case.