Is the word tempo the same in Brazilian and European Portuguese?

Yes

The word "tempo" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The vowels are generally more open, and the unstressed final "o" is clearly pronounced as a [u] sound (e.g., tem-pu).
• Continental Portuguese: The vowels are more closed and reduced. The unstressed final "o" is often very short, almost swallowed, and more neutralized (e.g., tẽp(u)).

Brazilian Portuguese examples:

1. Não tenho tempo para isso. (I don't have time for that.)
2. O tempo está muito quente hoje. (The weather is very hot today.)
3. Essa música tem um tempo muito legal. (This music has a very cool tempo.)
4. Faz muito tempo que eu não te vejo. (It has been a long time since I saw you.)
5. Preciso de um tempo para pensar sozinho. (I need some time to think alone.)

Portuguese (Portugal) examples:

1. Não tenho tempo para isto. (I don't have time for this.)
2. O tempo está bastante agradável hoje. (The weather is quite pleasant today.)
3. A música tem um tempo muito rápido. (The music has a very fast tempo.)
4. Já faz muito tempo que não te vejo. (It has been a long time since I saw you.)
5. Preciso de mais tempo para terminar o trabalho. (I need more time to finish the work.)