How can I cover PCB burn marks to identify burns later?

Non-reversible temperature-sensitive labels are available which will change colour irreversibly if they experience a defined temperature. These for example are 14 mm diameter which should be small enough to attach near one of your transistors, or even on the transistor itself.

Another option could be to slip a small piece of heat-shrinkable tubing over each transistor, maybe using a dot of cyanoacrylate glue to hold it in place. Standard heatshrink typically shrinks at somewhere between 70 and 120 °C, which is probably the range you would consider as overheating. If you observe that the tubing has begun to shrink, you know it's seen a temperature somewhere in this range. Note that anything that impedes airflow over the transistors could cause them to run even hotter, though.

Finally if you're concerned that these transistors run hotter than they should, you could fit them with clip-on heatsinks anyway as a precautionary measure. This will increase the stress on the solder joints and PCB tracks though, in case the equipment is likely to experience mechanical shock or vibration.

You could use a blob of wax on the components that you suspect are getting hot to see if it deforms due to the high temperature. Waxes come in many different melting points. For example, beeswax melts at about 62 °C.

If something is getting really hot, you could use hot melt glue, which melts at about 110 °C.

As user71659 pointed out in the comments, calibrated melting temperature crayons are available in temperatures from 40 °C and higher. See here and below.

Use a sharpie and draw some arrows, or circle the affected areas. Then use a thermal sensor from Home Depot to check temperatures. I have one like this, I think made by Ryobi, is great for all kinds of measurements around the house (Found with search for "infrared thermometer"):

https://www.homedepot.com/s/infrared%2520thermometer?NCNI-5

Might even be able to get a phone app that shows hot spots. Google "phone infrared camera app" I think most are an infrared camera that displays on your phone, I don't how good they'd be for smaller area views. The $35 infrared gun with laser pointer I know works well. Better than burning a finger! (done that too ...)