Certainly will not warm up in 4 miles if the isn't more than 10 minutes so a weekend of driving the car for an hour would be useful. Also recommend the CTEK or Deltran Battery Tender when parked at home not driven.
Should not harm the engine and if you are concerned pull an oil sample (Blackstone provides free sample bottles) and send it to Blackstone of lab of your choice to verify nothing is happening. At 7500 miles you should have sufficient total base number (TBN) which is a measure of additives to protect the oil which protects the engine. Other data is also useful like metal wear rates in ppm etc...