I try to hold my developer temperature to the target temperature ±1ºC. I try to keep my other temperatures as steady as I reasonably can but if they vary by ±5º over the span of a few minutes, I take steps to correct it.
Overall, the shock of a quick temperature change, regardless of the amount, can be worse than a temperature change that varies by several degrees over the span of five or ten minutes.
In the past, I have had accidents where I set my film down to rinse under the faucet then left the room. When I came back to check, I found that the water was almost ten degrees warmer than when I started. "Oh $hit," I thought! But that change took place over ten minutes or more. While not the best thing to happen, I haven't experienced any damage.