The drive cable is likely a red herring.
When you replace the drive the first thing that happens at boot is Spotlight (mdworker processes) index the drive. The high I/O rate of an SSD compared to a spinning drive permits these processes to run like gangbusters. The system that was not designed with such drive access speed in mind. Quite the other way around, the designers would have expected the spinning drive I/O limitation to be a natural throttle on CPU use during indexing.
You will find that users of older Macs tend to have accumulated more data so indexing has much more work to do than on a fresh OS i stall, and that when migrating after a fresh install, indexing is gated by migration speed. It’s users who clone a well-used existing system who will see a power surge at start up.
Once the Spotlight indexing completes, the high load stops.
This situation can seem alarming because Macbooks of all stripes are not intended to be run at full load due to power and cooling barriers. However they are designed to withstand it! You will find that Intel regards 100C as the top of the normal operation CPU operating range, and that a die temp of around 125C will force a protective shutdown. To human sensation, such temps seems astoundingly hot as you would be quickly burned if you touched a part at 100 C, but inside the CPU itself you’ve got a literal chip of sand and 100 C is nothing to it except a factor in a total system balance power. Worrying about it being hot is like worrying about water for tea being hot; just don’t spill it on yourself! As can be seen, coupling that hot chip to the outside world is a challenge, with small fans running fast to move sufficient cool air across a tiny radiator. So under high load the system is annoyingly noisy, the case gets hot, and the battery rapidly drains.
You might have noticed that at first start of a fresh macOS installation, a desktop notification warns about a temporary performance impact of drive indexing. Once the drive is indexed, only changes are tracked and Spotlight will no longer be a heavy burden.
You can test this explanation for yourself by using System Preferences > Spotlight : Privacy tab. Use (+) to add Macintosh HD to the list to stop indexing and delete the existing index, then (–) to remove it from the list so indexing starts over, just as happens behind the scenes at first boot after installing a fresh clone of a hard drive. Note fan speed for 10–20 mins. When fans speed up, use Activity Monitor to look at CPU usage and note “mds” and “mdworker” processes with high utilization. When indexing completes these will settle down and system will cool.
Spotlight indexing alone is a high load and causes racing fans. Other CPU intensive activities running at same time add to the load.
Problems with Spotlight loading may be even more problematic for aftermarket NVMe storage because it’s much higher performance than SATA. I have seen the NVMe drive itself overheat and die on a hackintosh.
So as to the concern that SATA drive data cables are a cause of bad thermals, this claim deserves more evidence than anecdotal observations about “data flows”. While it's true that the internet is “not dump trucks, but a series of tubes” it is not true that data cables get hot by being over-loaded. Nor can we assume the CPU is running data error-correcting checks on hard drive I/O. Drive CRC is not a function of the I/O channel to the drive, it is a drive-internal media function. There is no concept of a retry on internal bus errors like in networking, any more than there are RAM retries — there aren’t. In Macbooks, faulty drive cables typically result in device being fundamentally unreliable, not overloading. Also, there is no such factor as generational SATA cables, and even if there were we should expect Apple would supply SATA drive cables that match the generational revision of the controller in the Mac. So while the answers pertaining to purchasing new drive cables are appealing in the context of a drive cable supply co., there is not much technical substance to this suggestion. It could conceivably be true by some arcane law, but in the situation described in original post, it’s mist likely Spotlight.