The change between other measurements to using Celsius or Fahrenheit wasn't like the change from Fahrenheit to Celsius (or miles to kilometers), it wasn't a matter of people all having one pretty good standard and switching to another standard. In the 16 and 17 hundreds there were several different competing scales and no real standardization. You have to remember that at this time scientists were exploring the concept of temperature, ordinary people weren't using temperature in their daily lives. Indeed, in the early years you couldn't even buy a thermometer, you had to make one.

There were several competing standards, but in some regards it's better to call them experimental recipes or instructions on how to make thermometers. One of the big problems during this early period was how scientists could reconcile their temperature measurements and experiments with one another, which is how thermometers started becoming popular. One popular scale was the Delisle scale, which used a mercury thermometer and set the boiling point of water at 0 degrees and a fixed scale for the contraction of mercury below that (meaning this scale ran opposite to the ones we're familiar with), later this was recalibrated so that 0 was the boiling point of water and 150 degrees the freezing point. Newton also had a scale, which used the expansion of linseed oil, it fixed 0 degrees as the freezing point of water and 12 degrees as the human body temperature (along with some other measurements such as the melting point of wax in a bath tub, the temperature of iron glowing as brightly as possible, etc.). Then there was the Romer scale, which defined the freezing point of pure water at 7.5 degrees and the boiling point of water at 60 (originally it had been defined with the freezing point of a brine solution at 0).

This is just a sampling of the wide panoply of competing scales that existed at the time. Throughout this period of the early 1700s thermometers were generally hand-built research instruments, the definitions of the temperature scales were not just a matter of afixing the number scale in a particular way, they were a matter of defining calibration procedures. Many of the early scales had pretty "loosey goosey" calibrations. The choice of which scale to use for a given purpose was a matter of the convenience of construction and calibration as well as the desire for precision.

The Fahrenheit scale, introduced in 1724 fixed the freezing point of a brine solution using ammonium chloride at zero and human body temperature at 96 deg. Celsius main contribution to the temperature scale (in the 1740s) was to significantly improve the accuracy (and convenience) of calibrating thermometers by determining that the melting temperature of a pure water and ice mixture remains unchanged at different pressures and by determining the relationship between the boiling temperature of pure water and atmospheric pressure. Since barometers had been invented decades earlier and were now fairly common instruments this meant that it became remarkably straightforward to construct accurately calibrated thermometers. Celsius' work did much to transform experiments in thermometry from one with a lot of measurements that were kinda free floating relative to one another to one where they were all based on a fixed underlying scale based on precise calibrations, even if they used different units. Indeed, the Fahrenheit scale was changed after Celsius' research to fix the freezing point of pure water at 32 deg. F and the boiling point of pure water at sea level at 212 deg. F.

However, Celsius never used the "Celsius" scale, nor did anyone else for several hundred years. The scale that Celsius used was similar to that of Delisle, running from 0 deg. at the boiling point of water to 100 deg. at the freezing point. After his death a reversed scale that had 0 deg. at the freezing point of water became adopted, but this was known as the "centigrade" scale. The name it kept until the scale was renamed in 1948 (in honor of Celsius' hugely important contributions) with the first major push toward the SI system of units. Even today some folks still call the scale centigrade.

So, there are two answers here:

The "technically correct" flippant answer: they used centigrade before it was renamed to Celsius.

And the more historically accurate answer: there was a hodgepodge of wildly different systems with sometimes inconsistent or inconvenient to recreate calibration points.