Time to rebuild?

I had time for one minute of troubleshooting on my way to work this morning. Quick recap: engine starts right up when cold, but soon bogs down at idle until fully warm. Today after backing out of the garage I popped the hood and pulled on the rod coming from the choke thermostat. Every time I pulled on it, the idle came up and smoothed out. When I released it, it bogged down again. The block temperature was probably 50, ambient temp was about 45, and the engine had been running a minute or so. I'm not sure if this points to the thermostat or the choke pulloff.