Homeowner self service

I've never delved into a furnace service before. I did add the overflow pump onto the side of it.

Previously it has overheated. The thermostat goes blank, flame goes out, blower stays on for a few minutes after that. I had it serviced, maybe just a blower fan cleaning? Not sure what else is involved in maintenance besides the filter.

I have open eyes and ears awaiting some knowledge. Thank you in advance.