2005 Seat Altea slow to start when hot

One possible cause below....
That version of 1.9 TDI has a "feature" in the ECU mapping. (Also exists on some VW 1.9 TDI versions). When re-starting, if the ECU senses that engine is hot, then it requires that engine is turning over at more than 270 rpm before it will inject diesel (and hence start the vehicle).
After a few years use, the battery (or more likely starter motor) get a bit worn and cannot quite achieve the require starter motor turnover speed...hence no diesel is getting injected. The problem rapidly gets worse once it starts because of increased cranking.

Potential solutions are to replace starter and/or battery but expensive. There is no firmware fix from SEAT. There is a simple work-around called the "Hamman mod" too. This workaround usually works well. A 12v relay is used to insert a 2000 ohms resistor in series with the coolant sensor but only whenever the starter motor is running (ie it fools the car into thinking it is cooler just while it starts). Try google "hamman mod TDi warm start". One way to wire the fix is shown in picture attached. Drive the relay coil with 2 wires , one from Ground and one from the starter motor. ie, the 12v signal from the start solenoid. That way the relay switches whenever the starter motor is running.
The coolant sensor is on right side of engine, near the back bulkhead. You can cut into the loom about 5 cms back from the sensor connector. Access for this is much easier if air filter and large filter holder frame are removed. (the frame pulls up via a push fix grommet).
I am not endorsing that you cut into your wiring loom. I was apprehensive to cut into mine. However it is only a simple cut just beside a socket connector on one wire and (for me) worked well. No more embarrasing cranking.

It is possible that glow plugs may occassional be activated (due to fooling engine is colder than it is) but should be an issue.

Get a local mechanic/technician to wire the relay for you. I got mine done for 25 pounds- labour and parts.

Here is the wiring diag for Hamman mod. Picture upload failed first time