13 plate 1.6d various although probs related faults

Hello all, got a strange fault although suspect it’s all going to be related to cooling system but here goes.just bought a 13 plate 1.6 diesel. Runs sweet but after 20 mins it looses power briefly (probably about 30 seconds) during which time the temp gauge goes up, then seems to clear itself (assume it’s going into some kind of limp mode although no warnings on dash) I’ve also got no heating. Coolant level fine so no leaks . Someone suggested I try the water temp switch as only £15 which I have just done but was surprised when I took it out there was no coolant there. Is this correct. I’m thinking along the lines of an air trap in the coolant system. Tried running it for a while with the header tank cap off while idling but made no difference . Looking for brains out there to confirm/suggest the line I’m going down