What is tempered tuning?
Our common tuning is the equal temperated tuning. That means that the difference between every note is the same, the distance is mathematically seen the 12th root of 2. That means, after 12 halftones the frequency is doubled, as it is the next octave.
With this tuning system there are no very bad sounding intervalls at all on piano (but one could say also, no very good sounding intervalls). For instance if you play a quinte, you will hear a slight wobbling, maybe every second or so. If you play the quint a half tone higher, and proceed every half tone, you will realize that this wobbling gets contiously more and more, an octave higher the wobbling is doubled. At least that is the case in a perfect tuned piano.
Beside that there are historical temerated tunings with not equal intervals. Some sound worse, some better. Because some intervals have no wobblings, normally received as very strong and powerful chords. Others have so much wobblings that one needs to avoid those keys better.
To me it is problematic to give in the equal temperated tuning different keys a certain character. Because from the temperament all keys are similar (in opposit to the nonequal temperated tunings).
That's why it is problematic (to me) to e.g. associate d major with a festive character (only to mention an example). Already the fact, that some played 300 years ago d major a half tone lower or higher, so that means d flat major or e flat major were the keys in those days which must be associated with the character some refer with d major today.
The different character of different keys come in my opinion more from how often a key is used in general or for certain moods some personal "reference" pieces have in that key, but not from inherent character of a key. Because with equal temperated tuning, there is no certain character anymore of a certain key. By the way, I very much like historical tunings, there are some organs in Germany at which those tunings are used with success for certain baroque music.