Can solder be used instead of quick disconnect terminals?
Soldering this connection is illegal and unsafe; it's prohibited in AC mains wiring by NEC, and in appliances by the UL White Book; both proscribe conditions in which soldering is OK, and this is definitely not one of them.
Feel free to do exactly what they did: use uninsulated crimp terminals and then shrink-wrap over the works once it is crimped.
I get uninsulated crimp terminals by removing the insulation from insulated terminals.  There goes the temperature limit!
After you crimp it for a complete and secure physical and electrical connection, feel free to solder it also if you really want to. This is how NEC tells you to use solder.   You can't just hork-a-dork solder like you do on hobby electronics projects; this is a high-current connection.  Solder has a low melting point, so voltage drop across the solder is something that matters quite a lot.  And that makes the resistivity of solder matter a lot.  In this application it combines rather adversely with the high temperature operating conditions and high current.