Akuperma
Granted I never learnt hilchos Para Aduma. Although we did read it recently, so the recipe is still in my head. The only things I recall needing are (See beggining parshas chukas):
1) Para Aduma
2) A kohein
3) Etz Erez
4) Eizov
5) tolas shani
6) Mayim chayim
7) Some kindling to burn the cow
Thats it! (granted some are easier said than done)
Where does the beis hamikdash fit in? (I dont think you need old para aduma ashes either, but that does ring a bell, Beis hamikdash i’ve never heard of needing)
do you have a source?