How does a higher temperature when programmed in the FMGC affect REC MAX FL?
FMS calculates REC MAX in cruise by calculating temperature from actual OAT and TROPO inserted in INIT A page. It assumes standard -2C/1000ft until inserted tropopause altitude which after it uses constant temperature. 

During climb it calculates temperature profile from inserted tropo/temp. If your REC MAX seems to be off during climb check the inserted values. Also, when A/C reaches CRZ ALT entered to PROG page it starts to use measured OAT at once, so REC MAX can change suddenly if it was off in INIT A page.

Note that REC MAX is only function of A/C weight, TROPO and OAT. Cost Index does not affect REC MAX.