Overheating I noticed a leak under the car?

I would fill up the radiator and I noticed a leak under the car. I found that the small hose was not connected to the overflow tank. The plastic where the hose connected to it was broken off and the previous owner tried to connect it back together with glue and tape. So, I ordered a new universal water overflow tank. Now, If I am waiting for a light to turn green and it takes a little bit longer than usual, the temperature starts to get hot. Then when I start driving it the temperature will cool down. Please help me out with this one!