It may indeed be running slightly warm.

Besides the thermostat change, flush and fluid change, I would also take a moment to flush water back through the fins of the radiator (opposite of air flow) incase this car was driven down a dirt road regularly, it may just have hidden dirt in the fins. You may need to remove the fan shroud and don't use high pressure or you may bend the fins, high flow is ok. Make sure to flush the entire fin area. If this doesn't fix it, I would then look at my fan clutch, if yours is not electric, when the car is hot and you have shut it down for a few minutes (let it heat soak a bit), try turning the fan to see if it feels like there is sufficient resistance to provide proper cooling, if it turns too easily it is toast.

This can also be tested with a timing light, fully warm the car up, shut down for a few minutes, point the light at the fan, rev the car slowly to 3000 rpm, and see where the fan seems to no longer be keeping up with the engine, I think you should get around 3000 rpm out of it though it has been a long time since I have done this, a bad (or cool one) will quit much earlier. If you should need to replace it, there is an optional tropical version of this clutch as well as a tropical version of the blade section. Also there's a thermostat that will open a few degrees earlier. Recommend you only use Volvo thermostats, regardless, I would test the thermostat prior to installing, at least I would operate it manually compressing the spring slightly to verify that it works smoothly.

You could also have a radiator shop (or a Volvo repair center) pressure test your cooling system, even without leaks if your pressure is low or uncontrolled your temperature will rise slightly.

Also missing from a lot of older 240's is an air scoop attachment mounted under the bumper and behind the spoiler that directs air from the spoiler openings up into the radiator, replacing a missing one will help cooling. Though I am not sure if your year had one, certainly not if you don't have a spoiler.