How can I make creme fraiche quickly without waiting for it to curdle?
True creme fraiche is made by a biological process.  Within certain limits, fermentation may proceed faster at warmer temperatures, but in the end, you have to wait for the culture to grow and do its work of emitting the acid that thickens the cream.

I would be cautious of raising the temperature above more than a very warm room temperature, however.

My survey of recipes (you didn't provide the one you used) indicates that should be usable after eight to twenty four hours, but it will be thicker the longer you wait.  Even after the fermentation period, several recipes indicate that it will continue to thicken and improve for several more days under refrigeration.