Attempting to make this question the end all for "my furnace is blowing cold"
In my case, I had a furnace that just "blew cold" forever.
Turns out it didn't blow cold forever. Initially it would fire on, then shut off, fire on, shut off, 5x. Then blink 8 red blinks for an hour, while blowing cold air, then repeat. So I guess once/hour it felt slightly warm?
Seems for me this meant the flame sensor was bad (for a york/evcon anyway). Cleaning it (even though it looked pretty clean already) seemed to fix it.
8 red blinks apparently means "5 recycles in a call for heat". I think a "recycle in a call for heat" typically means it starts up "OK" then a few minutes later loses flame 'signal" so it tries to restart the flame (while still blowing the whole time). Which is apparently different than 7 red blinks, which is "failed initial startup 3x". Hypothesis: even though mine was failing "up front" maybe it thought it was working just initially?
Hypothesis: with the recycle kind of failure, it also leave the blower on for an hour while waiting to try again.
Tricky because this does cause the air to be "kinda lukewarm" as it were. But there will be no flame going while it blows...(which you can check for).
Also check if fan is on AUTO (i.e. always on) mode: https://diy.stackexchange.com/a/25677/11265
If there is no flame ever, check the high temp limit switch (if it's broken, no gas will flow at all, it acts as a safety to the gas valve).
If it's high efficiency furnace, condensate drain might be blocked. Turns out if the condensate drain "backs up" then it can plug the hole leading to the pressure switch. Wonder if that would cause a similar issue?
If you watch it and see flame start but later "sputter" as it goes out (high efficiency furnace) that might mean the condensate drain is blocked and the furnace is filling with water, and the water is interfering with the flame. Or an intake/outake pipe blocked. Which perhaps might cause this issue (flame goes out so sense is then lost, see above)...