Recently replaced thermostat on 2000 Subaru legacy outback. Now sometimes while driving it will overheat and heater blows cold then temp gauge will drop back down to normal and heater blows warm.

That sounds like a bad thermostat. Try it again.

It's a little more complicated than that: firstly, many aftermarket t-stats have SMALLER orifices than the OE Subie one, manifesting overheating in warm weather on longer highway runs. But before removing your new t-stat and verifying its size (and perhaps function on the kitchen stove), I'm going to guess that you didn't completely purge air from the system, which requires 2-5 heated runs and purging top hose air and topping of with coolant mix (sometimes one even has to elevate the FRONT of the car for a final topping to ensure the heater core ios purged fully). But if after you're sure the system is purged and you're STILL seeing alternating heatless and overheating gauge cycles, then indeed replace that "new" t-stat with a proper large orifice one. Of course you'll have to repurge again (sorry!). If after all this you still have this thermodynamic trampolining than it's quite likely that you have a cylinder percolating exhaust gases into the coolant, superheating a gas pocket near the gauge temp sensor alternating with one sitting in the heater core. In that event throw this antique away rather than chasing it with a new radiator, or of course, a proper, pricey ($1500-2k) HG job. But if you're certain that you had NO untoward thermodynamic nonsense BEFORE your goodwill t-stat changeout mistake, it's likely following my instructions above will work, and save you mucho bucks. But if you changed the t-stat BECAUSE you had coolant issues BEFORE your t-stat job, then I'm quite certain your HG's have a high pressure breach. So what's the chicken and what's the egg here?