pausing servo reaction to temperature sensor at transitions

Sorry if the topic title is confusing. I have a servo attached to a type-K thermocouple that reads temp from my wood stove . I use the servo to move the damper lever to 3 different positions based on temperature readings. When the temp is making the transition from one “position” to the next it takes a bit to move an jumps back and forth between the two commands. I am looking to eliminate that problem so that it will pause in its current position and wait until the temp is fully into the next area. Here is the code-

if(tempC < 199){
pos = 0;
myservo.write(pos);
}
else if(tempC > 200 && tempC < 260){
pos = 90;
myservo.write(pos);
}
else if (tempC > 261){
pos = 180;
myservo.write(pos);
}
else {
pos = 180;
myservo.write(pos);
}

Thanks for any ideas.

Make the gaps bigger than 2 degrees? But also take out the else, which will send it to 180 when it’s exactly 199 or 200. (It will go from 0 to 180 to 90 as it heats thru 199, 200 atm.)

Try (say) if <199 or else if >205 or 210 or something. Maybe stick a few seconds’ delay between readings?

Does your servo have adequate power to move the damper? does the servo operate as expected when not connected to the damper?