The batch size for most homebrewers has been around 5 gallons (19 L) for a very long time, and keeping this volume of fermenting beer cool is not difficult. Recently, however, many homebrewers have become interested in controlling fermentation and aging temperature and all types of fancy rigs are being built to make little fermentation cellars for use at home. To boot, batch sizes for many homebrewers has increased and the heat of fermentation is more difficult to remove in these larger vessels.
The short answer to your question is yes; there is a long history of fermenter temperatures moving up and down during fermentation. At one time it was common for tanks to be equipped with attemperation coils, or pipes inserted into fermenters for the purpose of temperature control. A fairly common method used for attemperature coil operation is to monitor the fermenter temperature with a thermometer and to simply turn the cooling valve on for enough time to cool the fermenter and then after some time the valve is turned off. This method of tank control is called “on/off” control and is how most thermostatic controls are operated. Since manually controlling fermenters with attemperation coils requires brewers to manually monitor and control fermenters the result is a temperature profile that moves up and down around the desired temperature.
Predicting how temperature affects flavor is not an exact science, but in general terms the effects of fermentation temperature on beer flavor are well known. Beer flavor is cleanest when the fermentation temperature is as low as possible for a given yeast strain without causing problems with sluggish and/or incomplete fermentations. As temperature increases the production of esters increases and fruity aromas increase, especially for beers made with strains that are noted for the production of aromatics. The production of these compounds is greatest at the peak of fermentation and it follows that the most critical point to consider for temperature control is this peak in activity.
Commercial brewers often begin fermentations cooler, usually about 5 °F (3 °C) cooler, than the controlled temperature, which you can try. One reason for allowing the fermentation to experience this “free rise” is that tank temperature is easier to control when the fermenter is being mixed by the activity of fermentation. After fermentation is complete the temperature is lowered. If you plot temperature over time the result is a curve that goes up and down.
To summarize, temperature fluctuations are normal and the most important temperature to control is the peak temperature experienced during peak activity. Also, starting cool and allowing your fermenter to warm up is a good method to consider if you lack refrigerated cooling. To keep the peak from getting too high you can use a low tech method such as plunging your carboy into an ice bath for 20 minutes or so at a time, a method that mimics turning on the valve of an attemperation coil.