The rate of heat production depends also on the power being used in the heating element, this power being measured in watts.

我认为，这两个 being 都不可省略。

从句意看：

“产生热量的速度”（The rate of heat production ）是一种“动态数据”。功率的被使用和被测量，也是动态的，自然是 “正在被使用” 和 “正在被测量”。

从结构看：作定语的 being done,  一定表达 “进行 + 被动”。

being used = that is being used 或 that was being used

used = that is used 或 that was used

being measured 同理。

比较：

The meeting being held now is of great importance. 现在正在召开的会议很重要。

The meeting held yesterday is of great importance. 昨天召开的会议很重要。

The meeting to be held tomorrow is of great importance. 明天要召开的会议很重要。