In my opinion, Yes, a sudden 6 degree temperature fluctuation (in either direction) will kill fish FAST. My method, that has worked perfectly for years, Aging my water. What I do for all my tanks is, for my 20 gallon I do 50% weekly W/C, which is 2 5 gal. buckets, filled and let sit in my bathtub 48 hours prior to W/C. The reason for this is the water straight from my tap has a PH of around 8.4, after it has a chance to sit, it settles to 8.0. Plus the chlorine has a chance to gas-out naturally (I still use seachem prime just as a precaution) so after all that your water is completely stable, I never use straight from tap, it only causes problems with fluctuations in my tanks. NOW temperature wise, Get yourself a meat thermometer ( I know how it sounds but bare w/me) they are shockingly accurate (I crossed tested against aquarium thermometers) test water temp. in buckets, for me, my aged water always reads 68-70F, so I plug the tub and fill with hot water about 1/3 up the side of the buckets, give the buckets a stir every 10 minutes or so, keep checking the temp. of the bucket water, in 20-30 minutes, my buckets temp. match my tank temp.