Seems like an odd way to go about things. The rise to room temp didn't do anything to improve flavor or quality in the short term. If it wasn't finished "cleaning up" off flavors, the yeast isn't going to do a very good job of it after it's gone dormant.
If you want to speed up the process and have better beer, let the secondary fermentation finish by leaving at room temp for longer and then crash/keg/carbonate/enjoy. If you're not worried about drinking it sooner and you want to improve the quality you should probably let it ferment longer than 10 days, anyway.
Typical "quick-to-drink" beer would be something like: Low gravity wort fermented fairly aggressively for 10-14 days, crash for 2-3 days to clear, keg and force carb at high pressure, serve.
A more quality-based regimen would be: Relatively low-temp, clean primary fermentation of 7-10 days to FG followed by secondary for same (either with transfer by racking or lengthening time in the primary vessel) for a total of around 21 days. Crash for up to a week to clear the beer, keg, carb, let sit for 1-3 weeks.
Some beers are quite nice served young and a 2-week grain-to-glass brew cycle will be fine. Most beers benefit from a total turn-around of 5-6 weeks, longer for lagers.