Fiesta Encore R reg?

My fiesta cuts out temporarily when I slow down from high speeds - sometimes I have to turn the key before I can accelerate again. It seems to be happening more often at the moment. Also the fans consistantlt blow out hot air even though it says cold so it's like an oven in there. I've checked my water and oil levels and the thermostat reads normal. Any ideas on these 2 problems? Thanks