Funnily enough, I often find espresso based coffees don't provide the same jolt in the morning, whereas coffee from a cafetiere does. However, keeping on topic, there is a lot of personal preference involved when it comes to coffee, and it could be that the taste isn't triggering that wake up moment for you.
As @Ecnerwal mentioned, there are "standards" regarding temperature which may or may not suit your tastes. Like @Ecnerwal, my approach to brewing coffee is to listen to the sound of the kettle. Sometimes I miss the cues and the kettle boils, in which case I add some cold water to the grounds before the boiled water. I find that, most of the time, I prefer coffee brewed at a much lower temperature than the "standard" as it has a deeper, heavier flavour, but go too low and it tastes flat to me.
Then there is brewing time. My basic approach used to be to grind 3 tablespoons of beans, add the water, wait ~1m40, one big stir quickly near the surface, wait ~1m40 and then press and drink. At some point I realised that the stir could be left out if I left the coffee to stand for longer (which makes sense based on how caffeine extraction works). The taste was equally satisfying, but 4 minutes without stirring just wouldn't do it for me.
Of course, there is the coffee itself. Whenever I get a new batch of coffee there is a degree of trial and error regarding time, quantity, temperature for me to get it right. Less so if I buy a blend, more so single origin. Different coffee has slightly different needs. Then there is the whole Arabica/Robusta/Other debate. Robusta seems to have a bad name, but you might actually prefer the taste and it generally has more caffeine content. One of the best coffees I have ever had was 100% robusta from a local roasters, and it certainly packed a caffeine punch.
Finally, the problem might not be a matter of coffee but a matter of ritual. That big sense of relief for me comes with the first sip of coffee, before it can possibly have had any physical effect. The very idea of having coffee does the trick. In no way dismissing your experience, it is possible it is the result of a changed perception towards your coffee, rather than the caffeine content itself.