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

No

While the meaning, spelling, and grammar of "quente" are the same in both varieties, there are significant differences in pronunciation and typical usage:

• Pronunciation: In Brazilian Portuguese, the unstressed final "e" is typically pronounced as a clear /i/ sound (e.g., kẽ-chi). In Continental Portuguese, the final "e" is much more reduced and "closed," often sounding like a nearly silent or very short /ɨ/ (e.g., kẽt).
• Usage: In Brazil, "quente" is commonly used to describe the weather (e.g., "O dia está quente"). In Portugal, while "quente" is used for objects or substances, the word "calor" is much more natural when referring to the temperature of the air or the weather.

Brazilian Portuguese Examples

1. O café está muito quente. (The coffee is very hot.)
2. O dia está muito quente hoje. (The day is very hot today.)
3. Cuidado, a comida está quente! (Careful, the food is hot!)
4. Essa água não está quente o suficiente para o banho. (This water is not hot enough for the shower.)
5. O sol está muito quente. (The sun is very hot.)

Continental Portuguese Examples

1. O café está muito quente. (The coffee is very hot.)
2. Hoje está muito calor. (Today it is very hot.)
3. Cuidado, a sopa está quente! (Careful, the soup is hot!)
4. Esta água não está quente o suficiente para o duche. (This water is not hot enough for the shower.)
5. A comida está demasiado quente. (The food is too hot.)