High Temp/High Pressure Readings in Boiler

We recently had a fill valve replaced (hot water boiler had low pressure). As the old valve was a dual fill/relief valve, we also had a new pressure relief valve installed on the boiler. However, subsequently we have had several occasions where 1) the safety button on the furnace kicks off the burner. The temperature gauge on the furnace outlet never reads above 100F, but the inlet pipe is clearly quite hot to the touch. (High limit is set to 180F, low limit for the pump to turn on is 100F, we turned it down from 120F) 2) the pressure gauge on the furnace outlet reads as high as 36psi, but with no spill from the pressure relief valve. Can we trust the relief valve would have spilled if the pressure really was this high and this is just a faulty gauge reading? We monitored by video tape and observed this pattern on several occasions.