Switching 12V/6A with an AVR – MOSFET or relay or both

Only partially related to question - using a hi side NPN as shown is somewhat unusual. It's certainly doable. You gate drive needs to swing from V_relay+ to typically 5 to 10 volts higher. If relay is say a 12V relay you will need say 17 to 20+ volts to drive gate (exact level depends on FET Vth etc). Use of a high side P channel FEt or a low side N channel FEt would be somewhat more usual. But, again, this is workable as is if needed.

D1 should be mounted as close to inductive load as possible. ON relay across coil contacts (or relay socket if used) is desirable. Any distance from inductive source gives a nice radiating loop.
Moving D1 around against the relay coil contacts will non-trivially reduce the radiating loop in the PCB track.

RC or RL decoupling the feed to the relay helps.
If same power source is used for thermocouple and relay then filtering in the thermocouple feed adequate to deal with any couple transients is needed. An active regulatopr will give typically 30 - 60 - ++ Vin noise rejection depending on model and design. Any RL or RC filtering in power circuit will add more filtering.

It's not obvious on the PCB how ground gets from the "Power" connector to the ground plane on the right hand side.
Any ground path commonality will help undo your good work. A milliohm of common ground return and a one amp spike will give you 1 mV of coupling. On a 5V supply that's 1:5000 coupling or about -70 dB. Not much, but it sets an upper limit to the isolation you can achieve. If you manage to couple that 1 mV directly into the sensor feed it will be much much worse.

A thermocouple usually has a thermal time constant of seconds at best and 10's of seconds often. You can get super fast response devices but they would be unusual. Low pass filtering the thermocouple or integrating over a few seconds will greatly diminish the effect of an occasional switching spike. If the spikes come thick and fast this will be less effective. A 10 mS spike in a 2 second integration period adds 10:2000 = 1:200 of it's magnitude to a signal or about -50 dB. Better not to be there at all BUT the effect will be small in many cases.

An ideal capacitor's voltage cannot change instantaneously. A good high frequency response capacitor on the relay side of the MOSFET will limit the inductive voltage spike while D1 is thinking about turning on.

One issue is that you do not have a fixed grounding resistor on the transistor. This may not always be needed. However the Uno ports are not programmed at reset or when there is no program running. In those cases the port may be set to a high impedance input with or with out a light pull up resistance. In this case you might be unknowingly turning the transistor on intermittently with noise or pull up leakage current.

To insure stable operation be sure to set the controlling port pin quickly to a digital output and set the initial logic value. Adding a resistor to ground, (before or after the existing 10k) will help prevent an open port or a light pull up from activating the transistor. With a 5v Uno a matching 10k should be OK. Lower resistor values reduce the chance of unknowingly activating the transistor, but at some point the high signal will not be able to turn it on.

If immediate switching time is not critical adding a small cap on the transistor base to ground can prevent fast multiple ON-OFF cycles that could reduce the life of the bulb. (Maybe 1uf).