You can warm up cold custard and it will turn out just fine as long as you warm or reheat the cold custard up correctly.
The best way to warm up cold custard is to warm the cold custard up in the microwave.
To warm up cold custard in the microwave put the cold custard into a microwave safe container.
Then cover the container that the cold custard is in.
Next turn the microwave on full power and heat it for 2 minutes.
During the heating of the cold custard be sure to stop the microwave halfway through and then stir it and then heat it some more until it's warmed up enough.
Sometimes it can take less than 2 minutes to heat the custard back up depending on the power and wattage of your microwave so watch it closely.