We have an older(at least 20 years that we know of) Sears series 600 furnace. Recently the blower started coming on for 10 to 15 seconds than shutting off. After 3 or 4 times of doing this furnace will run through a normal cycle. Also ,sometimes the blower will come on as soon as the burner lights without going through a "warm up" cycle like it has done for years. Any help or ideas are appreciated. Thanks.

https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html#post269001
https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html#post269005
My guess is a faulty fan limit control, here are pictures of the 2 most popular used, which one is in your furnace? If it is the Cam-stat I think that will be your problem.