That's not how heat and temperature work. Temperature isn't proportional to how much power your HDD is using. It's proportional to (power use) - (heat removal) integrated over time.
If you remove the HDD fan, that means it has to get rid of heat by passive air convection. This isn't enough. The HDD's temps will slowly climb until it's hot enough (heat transfer rate is proportional to temperature differential) that passive heat dissipation equals power consumption, or the drive does a thermal shutdown. Yes there is a provision for this in the firmware. I learned this the hard way - placed my two old HDDs on my desk with cables running to them, so I could copy the data to my new (much larger) HDD. Then left the room for a couple hours while the files were copying.
Based on the SMART logs, one drive shut down after reaching 63C. Forever after, it gave me SMART errors about its temperature threshold having been exceeded. I couldn't find a way to clear it so I ended up just throwing the drive away, since the error would always pause the computer when booting.
The other HDD "only" hit 55 C. It was probably saved because the first HDD shut down and stopped the file copy. These were temps the drives hit *outside* the computer, sitting on a desk in my room exposed to the room air (but no fan).
Give the HDD a fan. It doesn't have to be a very powerful fan - just a slight breeze seems to be enough. Most HDDs are cooled by putting them near an intake vent in the case, relying on the PSU fan (blowing air out) to draw air in over the HDDs. But if the case is ventilated on both sides, your other fans will not draw air in over the HDD. And it needs to have its own fan. The only way I'd use it without a fan is if you can set it up so the cross-ventilation goes directly over the HDD. And I'd still monitor the HDD temps closely for the first few days you're using it.