Answer
When the temperature varies, each instrument will become slightly out of tune, but for rather different reasons. Therefore they may not stay in tune with each other.
Work Step by Step
Suppose the temperature rises. The flute material expands, and the flute becomes slightly longer, changing the wavelength of the fundamental. The speed of sound also changes, which affects the resonance frequency of the air column in the flute.
When the guitar strings become warmer, the guitar neck expands and the strings expand, changing the tension and the natural frequency.
The mechanism by which each instrument generates sound does depend on temperature, so the instruments drift out of tune, but do not necessarily stay in sync with each other.
