Focus estate 64plate

Topped up the coolant level last week when we had exceptionally cold temps and level was non existent. 

Today when driving from start i noticed the engine temp needle jump up to just top back down to 60 before stabilising at its usual place. Tonight when driving home i put the dash test on and put it on engine temp setting. So from start it was from 3 then steadily climbed up 60+ before zooming up to 98, it then dropped back down to 62 before slowly climbing back up to 79 / 81. For a 30mins motorway journey it stayed at around this temp. When coming off motorway and driving urban it drop down to about 77, when stopped at lights dropped down to 73, before returning back up to 79 or thereabouts when reaching home.

I am assuming aa dodgy thermostat but was wondering what the hive mind says. If it is dodgy thermostat how much roughly would this cost to repair/replace?

Thanks in advance

Did you make sure you purged any air from the system? 

Is there an easy way to purge the air from system? Ive seen 2 videos on youtube, one showed the passenger headlight having been removed and getting to the pipe, the other was to jack up the car so the radiator was raised and purge the air whilst having the screw top off the reservoir tank