new core? and yeah the water pump could be the issue i am getting heat since my mechanic fixed it but he had a hard time getting it to work but far from perfect and he thinks its a heater matrix issue but recently i noticed a slow coolant leak from my car i had water pump replaced in 2015 but i was stuck out in ireland on holiday when it let me down which was not idea so not even sure if they put a good water pump in or not but every month i have to top up my coolant level to full again, the leak is slow but from what you say this could be related to the heat being not very good?