Temperature gauge and warning light reads “engine hot”?

Monday of this week the wife’s vehicle listed above, xk8 convertible, dash code produced a yellow light saying, “low in coolant”. After the car cooled off ii inspected and found a hole in one of the hoses (center going to left bottom). The coolant reservoir was indeed low. Ordered a new hose and it arrived Thursday. Today (Friday) I put the new hose on and filled the reservoir with new coolant and allowed it to idle, testing both the AC and heating systems. Both systems seem to be working properly. The wife takes the car to the grocery store (5 miles) and dash red warning light signals “engine hot” and temperature gauge peaks on hot. She pulls the car over and in about 5 minutes the temperature goes down to normal. This repeats itself on the way home. Car cools down and I check fluid and it’s at full.
Help, what caused it to run hot?