Because the subject and verb are both plural, the sentence's construction shows you cannot use a singular word, so
temper, mood and
disposition are not correct in this space. The only possible answer is "spirits".
The words are not in fact synonymous:
a good temper = the person has an equable/even temper
a good mood = The person is relaxed and content
a good disposition = The person has a good character
good spirits = the person/people are happy and cheerful
I am sure your English is improving all the time!