Measuring temperatures is not so critical as it is for cold process. Still, it's always a good practice to check if the lye water differs in temperature by more than 10ºC/ºF from oils. If yes, heat the oils a little bit or let the lye water cool down, to avoid volcano effects.
Pour the lye water into the oils. Mix well for a few minutes with a whisker.
Add the alcohol and mix well. Then add the glycerin. While you can add them seperately, I've previously mixed both ingredients in 1 pitcher.
Mix well for 10 minutes, then let it sit for 2 minutes. You can use an immersion blender, but it's not required.
The mixture will start to create a bit of foam/bubbles, and then will make a small "parafin-like" film at the surface. It will also smell something like jelly in the making. These are signs that the recipe is going well and your soap is saponifying.
Add the sugar syrup and continue to mix well.
If your soap is not showing the signs of saponification, or you are observing floating oils - the soap batter will look "oily" - , heat the mixture up to 60 °C and use an immersion blender on it for around 5 minutes.