Use LOW cooking temperatures and SHORT heating periods.
Whenever possible, add the yogurt at the end of the cooking period or just in time to let the yogurt mixture come up to serving temperature.
Heating yogurt can lead to separation and curdling. So if adding yogurt at the beginning cannot be avoided, stir a mixture of flour or cornstarch blended with a little water into the yogurt.
Another way to lessen the chances of curdling is to allow the yogurt to warm to room temperature before slowly heating it.
To keep the thick consistency of the yogurt, DO NOT STIR into other ingredients instead, fold the yogurt into the mixture.