If the furnace short cycled with temp set high then it would point to being a furnace problem......
BUT
it only short cycling when close to temp set point (and working fine at higher degree setting) points to t-stat being problem.
For $20-$25 pick up a battery operated digital t-stat (Hunter is used a lot) and replace your t-stat.
Set it for 65*F furnace will stop at 66*F and come back on at 64*F
Some 1*F diff. for A/C operation
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
2007 HitchHiker II 32.5 UKTG 2000W Xantex Inverter
US NAVY------USS Decatur DDG31