Tefillin are usually thought of as coming in sets, one for the hand (shel yad) and one for the head (shel rosh). But is there any reason two sets can't be mixed and matched? May one wear tefillin where the shel yad and the shel rosh come from different sets? Does it make a difference if this is a temporary measure?
It is permitted.
A problem of כסדרן may appear - Rm"a addresses this (OC 32:1) and says it should be taken care of לכתחילה, but if not it's not פסול.
Regarding Rashi & Rabenu Tam - it would be contradicting to wear Yad of one and Rosh of another. However, Rabbi Ya'akov Medan says it is לכתחילה to wear rashi for Yad and Rabenu Tam for Rosh.