Briefly... for an analog pass transistor application, you need an FET optimized for operation in its linear region. Most today aren't, since FET's are so commonly used in PWM circuits where they are either fully off or fully on and thus minimize their dissipation. The manufacturers chase the sales volumes. But they're available if you dig a bit.
This information can be found under SOA (Safe Operating Area), if there is a curve given for DC it is rated for linear mode, but there are very few modern Mosfets that are rated for this.
IXYS has a series of special linear mode optimized ones, but not cheap.
Mosfets for audio amplifiers should be suitable as well.
You have to cool ~100W and let the mosfet stay quite cool to be in SOA.
A tough challange if you have to deal with higher environment temperatures.
To get an impression look at the teardowns of electronic loads...