How do you change a heater core on a 64 thunderbird?
If you can't get through the firewall to the heater core, then you will have to go from under the dash and possibly through the glove box.
Check the firewall carefully for any type of access panel. I've taken out the blower motor once to get at the heater core, think that was a Caddy.
You might be able to get a Haynes Manual for that.