厳密: a slight difference in meaning and precise temperature control
Distinguish a strictly qualified judgment about word meanings from the obligation to control room temperature precisely during an experiment.
Precision in a judgment and in control
厳密 (げんみつ) means rigorous or precise. The word-meaning sentence qualifies a careful judgment; the experiment sentence concerns the precision required in controlling room temperature.
厳密に言えば introduces what follows as a strict way of speaking. 厳密に管理する describes how control is carried out. Identify whether precision concerns a judgment about meanings or the management of temperature.
A slight difference and a control obligation
「厳密に言えば、その二つの言葉は意味が少し違う。」 (Strictly speaking, those two words have slightly different meanings.) Strictly speaking, the two words have slightly different meanings. 少し違う limits the degree of difference, without making their meanings completely unrelated.
「実験では室温を厳密に管理しなければならない。」 (The room temperature must be precisely controlled during the experiment.) Room temperature must be precisely controlled during the experiment. 管理しなければならない states an obligation, without reporting completed control, experimental success or a specific temperature.
Retain the qualification and the obligation
The first sentence supplies a slight meaning difference under a strict qualification. The second supplies a requirement for precise control of room temperature. Keep the target of 厳密に with speaking or controlling.
Preserve both the degree in 少し and the obligation in しなければならない. Strict speaking invites a careful distinction in meaning, while the control requirement identifies the precision the action needs.
What do the judgment qualified by 厳密に言えば and the requirement for precise temperature control express?
Show the answer and why
The first is a judgment that the words have slightly different meanings when speaking strictly. The second is an obligation to control room temperature precisely. Completely unrelated meanings, completed control and experimental success are not supplied.

