Well it will not damage the engine to run it at 3/4, which is why red is where it is, and the distance from 1/2 to 3/4 is shorter than the distance from 3/4 to red, however that is not the optimal temperature for ideal combustion in an engine. You are safe, but nevertheless, it never hurts to do all the tests that bmw_lvr has suggested that you do.
When you top up anti freeze, bleed the radiator according to the bentley manual (please search for the download), but prepared to see air pockets coming out and manifesting itself as falling coolant levels in the expansion tank. I had this for 3 weeks after I changed a radiator and bled it twice perfectly. Our systems trap air well and it takes time for that to be fully evacuated to the radiator. So please monitor coolant levels daily until it stabilises, and topup if it falls below the cold mark when the engine is cold.