PC12 Captain reported erratic oil temperature indications resulted in deviation to nearby airport.

Narrative

At cruise altitude FL250 engine oil temperature first fluctuated up and down within limits then suddenly spiked causing a red engine oil temp CAS. I Immediately retarded power and oil temperature returned within limits but with the power retarded oil temperature suddenly rose again but since my hand was on the power control lever it only caused the yellow engine oil CAS; crew alerting system. Each CAS immediately extinguished when power was reduced. Originally power was set at charted TRQ; [torque]; approximately 29.0 psi. -21 at 25000. After second power reduction power was at 22.0 psi Engine oil temperature was stable at 68; TRQ was 22.4 oil pressure was 121 psi. Per the Quick Reference Handbook (QRH) it appeared we could continue and ZZZ1 was really the only full service airport nearby and it was still 70 miles in front of us so we continued with the reduced power setting.In a very short time; less than 10 minutes with the power still set to 22.4 the oil temperature again spike. This time the temperature did not stabilize until the power was at approximately 15 PSI. With ZZZ1 only about 50 miles in front of us and a lot of nothing between there and ZZZ2 I thought the best course of action was a precautionary landing. [Requested handling priority] with ZZZ; received a clearance to ZZZ1 and the First Officer (FO) made a normal approach and landing on Runway XX. Engine oil temperature was normal and stable on the ground so we taxied to FBO and shutdown. Post flight revealed no apparent oil leak and the oil level was approximately in the middle of the sight gauge (where it was; on the prior 2 flights)