I pull a 7k stump grinder up and down the road just about every day M-F on a dual 7k per axle trailer.
I inspect how warm they get by touching after a 15 to 30 minute drive or when I stop for fuel. If you can touch without burning your hand you will not have an issue. Just be careful and put your hand close not touching, if no heat radiating do a quick touch, if not hot then feel longer for a warm axle.
Without a baseline or if you have not inspected them before inspect all axles by pulling off the end caps. If you are one of the lucky ones they will have a grease cert in the end of the axle(or a place to put one). Pump some grease in and inspect the grease coming out around the outside of the bearings. If no cert you may need to remove one tire and hub to inspect the condition of the grease. If it's clean no metal flake no water put it back together and re-grease. Over greasing every so often helps purge old grease/metal/water out. Just clean up the mess it makes.
Test each hub/bearing and axle fit by wiggling in on one side and out on the other side of the tire then top and bottom. There should be no play felt! If there is tighten the castle nut till the play is gone. I usually tighten until I can feel rolling resistance (too tight) then loosen 1 or 2 slots of the castle nut or until the tire turns free again. Keeping play out of your bearing set is as important as the grease. Too tight and sufficient lube can not get under them too loose and the bearings can chatter or bounce around. Remember to replace the carter key.
I have ran and maintained several trailers this way with no issues. Some I pull every day some set for months between use. and have not replaced bearings for over 5 years.
I bet the guy broke down on the side of the road getting a spindle welded on did not maintain/inspect his wheel bearings.
Get you some 9mil black gloves from harbor freight, high temp grease, rags and get in there.