Mine did that the first break in too. You should let it cool and then do it again but go through the speeds slowly.
With a new spindle you don't know for sure if the preload or bearing are correct so you need to watch it.
Were you breaking it in at low speed?
Move the gear sectors by hand to find a place where the machine will be in between gears and have no drag on the spindle. Turn the spindle by hand. It should turn 100% smooth with only the slightness drag. If you cant turn it by hand something is wrong.
It if feels OK then put the head in low gear and run it for 15 minuets or so watching the temp all the time. It should not get more than warm on low.
Do this for all the speeds.
I let mine run at 1000 RPM for a few hours after the first break in.
The first run at high speed the head will get much hotter than normal but it should break in and run cooler over time. You do need to make sure the spindle is not allowed to get over 160 deg or so for break in. If you are going by touch you should be able to touch it but not hold you hand on it for more than 5 seconds or so. Burning hot is not OK.
My head ran hot for a few weeks. The whole head and motor would get smoking hot after an hour of heavy milling. I changed out the oil in the head with Mobil 20W50 synthetic oil and the head now runs much cooler.