Overheating mystery

Hi everyone,

New to the community. I drive a 2005 Honda Civic.

My first question; Is anyone here familiar with a 'pebble system?'

To make it concise; my temperature gouge would rise toward the red zone. I then took the car in to my local mechanic about 6 months ago, and there is a crack in my head gasket that had caused a leak. Their solution was to execute a "pebble system", that basically fills in the crack to prevent any leaks, to my understanding.. ?

Since then, the car has been in shape and takes me to work (2 miles), but it will INCONSISTENTLY overheat. In other words, it appears to overheat whenever it pleases. I drove 12 miles to family for thanksgiving with no issue at all. However, this evening, I drove 2 miles to the store and the temp gauge was shooting up. It then shoots back down to the normal level if I hit the gas (It is winter here luckily, and the cold helps cool it down).

I am seeking any assistance, questions, and thoughts. I would appreciate any ideas, and i'm grateful for this community here. I really love the car.