In a nutshell, if you want to maintain the same level of carbonation when raising temperature, then you'll need to increase the pressure applied. Similarly, when cooling, you'll need to reduce the pressure by venting some of the CO2 in the headspace.
Although the CO2 pressure inside the keg will naturally increase with the higher temperature, the rate of solubility decreases faster, so you need to apply more pressure to maintain the same volumes dissolved CO2. If you don't, about 40% of the dissolved CO2 will come out of solution and build up in the headspace as you increase from 35F to 65F. See here for a detailed analysis of CO2 pressure and dissolved volumes, in particular Figure 3.1 which shows a graph the ratio of volumes to pressure over a range of temperatures - at 35F is about 0.10, while at 65F it's 0.06. So, if you didn't add any CO2 you'd get only about 60% of the carbonation level you want.
The converse is true when you chill the beer - since it was carbed at a higher pressure, and then chilled, the volume to pressure ratio is now higher at the lower temperature, and so you get more volumes of CO2 dissolved. This is easily fixed by bleeding the excess pressure from the keg over a course of a few days.
There's no long-term negative affects on your beer, although according to Charles Bamforth, the rate of oxidization increases by 3-fold for every 10C/18F increase in temperature, so the beer will oxidize faster at the increased temperature, but at these temperatures oxidization times are measured in months, so in practice I doubt you'd notice if only keeping it at room temp for a couple of weeks.