The old system DMMs (19" wide) were generally limited to the basics: AC/DC voltage, resistance and if you're lucky current. Fluke even had a meter where only DCV was standard, everything else (ACV, resistance) was optional. I guess that was useful back when these features were expensive if you needed a dozen meters to measure resistance.
The temperature feature that you'll find on older bench meters will generally be RTD or thermistor based. I.e. resistance measurement with some math to convert it to temperature. Don't expect to plug a type K thermocouple in there.
The lower end bench meters with less resolution, i.e. the Fluke 8000 form factor, would sometimes have more features like continuity and diode test, since these were often used for field service work before the handheld became powerful enough to handle those tasks. These were generally limited to 4.5 digits of resolution. I think the HP 34401A and the Keithley 2000. I believe of those two only the Keithley supports cheap thermocouples.
Do you really need to combine these features in the same box? You don't really need 6.5 digits for temperature or continuity.